SUMMARY Every qubit announcement invites the same question, and almost nobody asks it: what, exactly, is for sale? This paper argues that the product of a quantum computer is not a qubit, a circuit or a benchmark score. It is a verified answer, delivered into a customer's workflow, at a price below the value it creates. Judged by that standard, no publicly documented gate-model machine has yet passed all five gates that define a compute market: a correct result, a faster complete workflow, a lower complete cost, an independently verifiable output and a customer who pays for it twice. That is not a forecast of failure. The technical evidence of the past two years is the strongest the field has produced. Google ran a surface-code memory below threshold [1]. Neutral-atom groups distilled magic states on encoded qubits and teleported logical information [2, 3]. Quantinuum shipped a 98-qubit trapped-ion machine with 99.92 percent two-qubit fidelity [4] and, in 2026, showed logical error rates up to 800 times below physical ones on small codes [5]. These are machine-level advances. None is an application-useful logical computer, and the arithmetic in this paper shows how far the gap still runs: a computation with a trillion fault locations needs logical error near one part in ten trillion, which at today's measured error suppression implies code distances near 60 and roughly 8,000 physical qubits per logical qubit. Three complete-machine models translate that arithmetic into money. An early fault-tolerant instrument with about 150 logical qubits costs $17,000 to $40,000 per machine-hour. A commercial scientific machine with 1,500 logical qubits costs $80,000 to $320,000 per hour. A cryptographically relevant machine spends $4 million to $14 million per five-day factoring job. A widely cited catalyst calculation, valued at $200,000 and priced at 139,000 QPU-hours [9], tops out at $1.44 of gross value per hour. The physics is fine. The value density is not yet there. The investable conclusion is conditional rather than dismissive. Own scarce components with adjacent markets, platforms whose quantum program is a cheap option inside a larger business, and hardware teams that publish system-level evidence. Do not pay for physical-qubit counts as if they were capacity. Revalue the sector when five things move together: logical error keeps falling as codes grow, logical circuits get deep, uptime is measured in production jobs, magic-state factories run continuously, and a customer buys a verified result more than once.
1. Start with the unit of analysis
Ask what a quantum computing company sells and you will hear about qubits, fidelities, roadmaps and, lately, logical qubits. Ask what a customer buys and the answer is different. A customer buys an answer they can act on, delivered in time to matter, at a price below what the answer is worth. Everything in this paper follows from taking that second answer seriously.
The five gates make it concrete. A quantum result counts as a product only if it is correct; if the complete workflow, including data preparation, queueing, error correction, repeated sampling and verification, is faster than the best classical alternative; if the complete cost is lower; if
someone other than the vendor can check the output; and if a customer pays for it, then comes back and pays again. Any omitted stage is a hidden liability. A kernel that is a thousand times faster but sits behind a six-hour queue and a week of verification is not faster.
It helps to see how many rungs sit between a physics demonstration and a market. Quantum supremacy means a device performs a formal sampling task beyond a chosen classical method. Computational advantage means the best available quantum workflow beats the best available classical workflow on a defined metric. Practical advantage adds useful inputs, useful outputs and reliability. Economic advantage adds complete cost. Commercial advantage adds a buyer, a contract, integration and repeatability. The rungs do not collapse into one another. Random-circuit sampling can demonstrate exquisite control and zero customer value. A scientific calculation can beat exact classical simulation and lose to an approximation. A cheaper kernel can lose after state preparation and verification are charged. A successful pilot can fail to become a repeatable product.
The classical rung also moves while you climb. IBM's 127-qubit "utility" experiment in 2023 ran circuits beyond brute-force simulation; within weeks, sparse-Pauli and tensor-network methods reproduced the key results faster on ordinary hardware [10, 11]. Classical simulation later overtook early random-circuit sampling claims on a cluster of 1,432 GPUs [12]. In 2025, D-Wave's peer-reviewed claim of beyond-classical quantum simulation drew a tensor-network response that was itself published in Science in 2026 [13]. These reversals are not embarrassments. They are the adversarial process working as intended, and any resource estimate that does not budget for them is optimistic by construction.
So before admitting any workload, this paper requires quantitative answers to nine questions. What is the input, including data movement? What exact output is purchased? What is the strongest classical baseline? Which quantum algorithm applies? What logical resources follow after compilation? How is the output verified? What precision changes the decision? What does one verified result cost? Who pays repeatedly? A device may have excellent fidelity yet too few qubits, enough qubits yet too little depth, enough depth yet a six-hour cloud queue, or a beautiful sample that cannot be checked without doing the classical work it claims to replace. The nine questions catch each substitution.
2. What a quantum computer can and cannot do
A classical bit is in one of two states. A qubit is described by a complex amplitude for each of its two basis states, with the squared magnitudes summing to one. For n qubits, the joint state is described by 2^n complex amplitudes. That growth is mathematically real and almost entirely unreadable, because measurement returns a single classical outcome sampled from the state, not the amplitudes themselves.
This rules out the most popular explanation of quantum speed. A quantum computer does not try every answer in parallel and read off the best one. Most of the amplitudes are never accessible. An algorithm gains power only by shaping amplitudes so that interference concentrates probability onto an outcome you want to observe and cancels the ones you do not. Problems without exploitable structure receive no speedup at all, and complexity theory backs this up: quantum computers are not believed to solve NP-complete problems efficiently. The word "optimization" carries no exponential entitlement.
The algorithms that matter each exploit a specific structure, and each carries a specific tax.
Shor's algorithm turns factoring into period-finding and estimates the period with a quantum Fourier transform. The speedup over the best classical factoring methods is asymptotically dramatic, the output is compact and cheaply verified by multiplication, and the price is an enormous fault-tolerant circuit [43].
Grover's algorithm cuts unstructured search from N oracle queries to about the square root of N. The gain is quadratic, not exponential, and each oracle call must be implemented reversibly, forward and backward. For realistic N, parallel classical hardware, memory bandwidth and specialized chips erase much of the advantage [43].
Quantum phase estimation extracts the eigenphases of a unitary. Paired with Hamiltonian simulation it delivers energies, dynamics and material properties with precision that depends on the amount of coherent evolution available. Higher precision requires more coherent work, and useful long computations require reliable operations [44].
Amplitude estimation offers a quadratic reduction in samples for estimating probabilities or expectations: ideal amplitude estimation can use quadratically fewer coherent calls than classical sampling for comparable additive error. The gain disappears if preparing the state, doing reversible arithmetic and correcting errors costs more than the samples saved [45].
Quantum linear-system algorithms can depend only polylogarithmically on matrix dimension. They also depend on sparsity, condition number, state preparation, precision and what you ask for. They return a quantum state proportional to the solution, not the solution. Reading out N entries still costs at least N.
Hamiltonian simulation is the workload family most naturally aligned with the hardware, because nature already evolves quantum states. Digital algorithms approximate that evolution with product formulas or qubitization; analogue simulators engineer a controllable physical Hamiltonian directly. The digital path buys programmability and error correction. The analogue path reaches larger systems today at the cost of verification and flexibility.
The economically interesting set is therefore narrower than the set of things quantum computers can do in principle. It contains tasks with expensive classical baselines, compact inputs, compact outputs, high value per answer, tolerable precision, feasible verification and repeat demand.
Factoring fits the computational pattern and produces an attack rather than a service. Chemistry may fit, but only in strongly correlated regimes where classical methods fail and where the answer changes a decision.
Algorithm background: IBM Quantum: the phase-estimation procedure and Brassard et al.: Quantum Amplitude Amplification and Estimation.
3. A quantum computer is a control plant
Strip away the branding and a quantum computer is a control plant built around a fragile nonlinear system. The processor holds the physical degrees of freedom. Classical electronics synthesize pulses, time them, receive measurements and update later operations. Calibration maps intended gates onto imperfect hardware. A compiler schedules gates around connectivity and crosstalk. A decoder turns a stream of error syndromes into corrections. The qubit is the smallest part of the machine.
The stack begins before the qubit. Material purity sets dielectric loss, charge noise, nuclear-spin noise and optical loss. Fabrication sets frequency collisions, junction variation, defect density and yield. Packaging sets stray microwave modes, heat flow and serviceability. A high-fidelity laboratory qubit is not a manufacturable array, and the distance between them is where most of the capital goes.
Control is itself computation. A superconducting processor receives shaped microwave and flux pulses on nanosecond schedules. An ion system shuttles ions between memory and gate zones, cools their motion and drives optical or microwave transitions. A neutral-atom machine rearranges atoms with optical tweezers, tracks loss and coordinates parallel laser pulses. A photonic machine synchronizes emission, routing, fusion measurements and feed-forward. Calibration burden grows faster than channel count when parameters interact: pairwise crosstalk alone creates on the order of n² relationships to worry about, even when only a sparse subset matters.
Measurement is not a free terminal step. It has latency, infidelity and back-action. Error correction requires measuring stabilizers repeatedly without measuring the logical state, mid-circuit measurement fast enough for feed-forward, reset that prepares ancillas for the next cycle, and leakage detection before a leaked qubit poisons its neighbours.
Two software layers sit above this. Error mitigation estimates an ideal result from noisy runs by extrapolation, probabilistic cancellation or symmetry checks; its sampling cost grows rapidly with noise and depth, so it helps bounded circuits and cannot rescue long ones [46]. Error correction encodes logical information across many physical components and repeatedly extracts syndromes. A million-qubit surface-code machine emitting roughly one syndrome bit per check qubit per microsecond produces on the order of half a terabit per second of raw data before compression. The decoder must keep pace with that or the machine drowns in its own diagnostics.
Then there is magic. Clifford gates are comparatively cheap under stabilizer codes, and they are also efficiently simulable on a classical computer, which is exactly why they are not enough. Non-Clifford gates such as T gates supply the missing ingredient, and in most architectures they are supplied by distilling many noisy "magic states" into fewer clean ones. Factory area and throughput can end up defining the whole machine [48].
Above all of that sits classical orchestration: preparing inputs, choosing circuits, running optimization loops, managing queues, aggregating samples and verifying outputs. Cloud delivery adds authentication, scheduling, compilation, data governance and service levels. The customer sees an API and a result. The provider operates vacuum pumps, refrigerators, lasers, calibration services, spare parts, compiler versions and billing. A useful quantum computer is a vertically coordinated industrial system, and it should be valued as one.
4. Eight ways to build one
No modality wins every variable. Fast gates come with short coherence. Long coherence comes with slow measurement. All-to-all connectivity saves swaps and constrains parallelism. Room-temperature photons still need cryogenic detectors. Foundry compatibility coexists with immature yield. Table 1 summarizes the positions; the paragraphs below explain them.
Superconducting circuits are lithographed nonlinear circuits, usually transmons, operated at tens of millikelvin. They offer fast gates, strong electrical control and mature microwave engineering, and they are the only platform to have run a surface-code memory clearly below threshold at distance seven. Google's Willow result and IBM's Heron and Nighthawk processors make this the most developed fast-cycle path to fault tolerance [1, 14]. The liabilities are fabrication variability, crosstalk, leakage, wiring and cryogenic heat. Coherence sits in the tens to hundreds of microseconds; two-qubit gates take hundreds of nanoseconds. A million-qubit system cannot carry a unique room-temperature cable per function, so scaling hinges on yield, multiplexing, cryogenic electronics and code layouts tolerant of dead qubits.
Trapped ions use long-lived atomic states. Their uniformity, fidelity and local all-to-all connectivity reduce calibration variation and routing overhead. Quantinuum's Helios, published in Nature in 2026, offers 98 barium-ion qubits at 99.92 percent two-qubit fidelity in a quantum charge-coupled-device architecture that shuttles ions between zones [4]. In the same year Quantinuum and Microsoft reported logical error rates 11 to 800 times below physical rates on small codes [5], and a preprint on Helios reported dozens of error-corrected logical qubits with beyond-break-even logical gates [26]. Gate and measurement times run from tens of microseconds to milliseconds, so the commercial strength is quality per qubit and the weakness is throughput: a machine can have superb fidelity and still deliver too few logical operations per second for deep workloads.
Neutral atoms are held in optical tweezers and entangled through Rydberg interactions. Arrays are assembled from identical atoms, rearranged around defects and driven in parallel, and reconfigurable geometry suits high-rate codes and logical movement. The Harvard, MIT and QuEra collaboration reported below-threshold repeated correction, logical teleportation, mid-circuit qubit reuse and, separately, the first logical magic-state distillation [2, 3]. Atom loss is both liability and information: a detected erasure tells the decoder where the error happened. Loss, laser power, optical access and slow readout remain the constraints.
Photonic systems move easily, interact weakly and network naturally. Their liabilities are loss, nondeterministic entangling operations, source quality, switching and detector efficiency. PsiQuantum's 2025 Nature paper reported 99.98 percent state preparation and measurement, 99.22 percent fusion fidelity and 99.72 percent chip-to-chip interconnect fidelity, all conditional on photon detection and therefore excluding loss [16]. That qualifier is economically decisive, because loss expands source, switching and code overhead. Xanadu demonstrated modular networking across 35 photonic chips in its Aurora system [17] and went public in March 2026 [32]. Manufacturing leverage is real, but millions of sources, switches and detectors must work as a timed yield system rather than as isolated champions.
Silicon spins encode information in electron or nuclear spins. They are tiny and semiconductor-compatible, which is a credible density and manufacturing thesis. Diraq and imec reported two-qubit unit cells fabricated on a 300-millimetre line with single-and two-qubit fidelities above 99 percent, readout up to 99.9 percent and relaxation times up to 9.5 seconds [18]. The scale evidence is still small. Device-to-device disorder, charge noise, valley splitting, cryogenic readout and dense wiring remain unsolved at useful array sizes.
Bosonic and cat qubits store information in many levels of an oscillator, correcting the dominant error within one mode and then applying a smaller outer code. Yale demonstrated real-time correction with a 2.27-fold lifetime gain [19]; Alice & Bob reported cat-qubit bit-flip times above ten seconds [20]; AWS's Ocelot ran a distance-five repetition code of cat qubits below threshold, though still at about 1.65 percent logical error per cycle [21]. Hardware efficiency is promising. Application-ready fidelity is not yet demonstrated.
Topological qubits seek protection from nonlocal encoding in exotic quasiparticles, with the prize of much lower correction overhead and an evidentiary burden to match. Microsoft's Majorana claims remain disputed: a 2026 Matters Arising in Nature challenged the robustness of the topological-gap protocol used as evidence, Microsoft replied, and a "Majorana 2" announcement in June 2026 arrived without peer review [22]. No topological logical qubit has demonstrated a universal fault-tolerant operation. Treat the category as high-optionality research and demand reproducible non-Abelian operations before assigning it capacity.
Annealers and analogue simulators do not run a universal gate set. D-Wave's Advantage2 offers more than 4,400 annealing qubits [24] for hybrid optimization and quantum simulation, and mapping, embedding, precision and temperature determine the effective problem. Analogue simulators engineer a Hamiltonian directly and reach scientifically interesting scales sooner
because they skip compiling every interaction into gates; the price is scope and verification. Claims of annealing or analogue supremacy remain baseline-sensitive, as the 2025-2026 exchange between D-Wave and the tensor-network community showed [13]. The right commercial response is instance-by-instance testing on full customer objectives.
Table 1. Hardware modalities: demonstrated state versus scaling thesis. Ranges are indicative, not procurement specifications; gate definitions and benchmarking methods differ across vendors. Demonstrated Two-qubit Dominant Economic Modality scale quality Native speed Connectivity scaling burden Logical evidence posture Superconducting 100-156 high- ~99.5-99.9% 0.1-1 µs gates local lattice wiring, yield, below-threshold leading fast- quality gate- crosstalk, d=7 memory cycle path model qubits cryogenics Trapped ion 98 (Helios) 99.92% 10 µs-ms all-to-all within laser stability, small-code FT quality-led, zone plus transport, gates; 11-800× throughput- transport throughput logical limited suppression Neutral atom hundreds ~99.5% µs gates, slow reconfigurable loss, optics, below threshold; strong code-rate controlled; 448 readout/reload continuous many logical option in FT architecture reload blocks; magic- state distillation Photonic networked 99.22% fusion propagation- network-native loss, sources, architectural; manufacturing modules; (conditional) rate switching, limited logical and networking component detectors compute option demos Silicon spin 2-qubit foundry >99% ns-µs local disorder, none at scale density and cells readout, foundry option control density Bosonic / cat few encoded bias- µs local modules complex break-even lower-overhead oscillators dependent control, ancilla memories; option faults concatenated code below threshold Topological prototypes; not unknown architecture- proving the none research option disputed established dependent quasiparticle Annealing 4,400+ qubits not µs anneals sparse Zephyr embedding, not gate-model present niche comparable graph precision, service thermal effects
5. Error correction is the machine
Physical-qubit count is inventory. Logical capacity is productive capital. The conversion rate between them depends on physical error, error correlation, code family, target circuit volume, connectivity, decoder quality and gate set, and it is where most qubit-count headlines quietly die.
For a rotated surface-code memory, a first-order footprint is about 2d minus 1 physical qubits per logical patch, where d is the code distance [47]. Distance 7 uses about 97 data-and-measure qubits before leakage handling and layout. Distance 25 uses about 1,249. Distance 31 uses about 1,921. Routing lanes, boundaries, spares and factories push these up.
(d+1)/2
An approximate logical-error law reads p ≈ 0.1 (p/p ), where p is physical error and p the
L th th
threshold. It is a sensitivity tool, not a prediction: real devices have biased, coherent, leaky and correlated errors, and the threshold depends on circuit and decoder. A machine barely below threshold needs a large distance for modest suppression.
Google's measured numbers make the issue visible. At distance 7 the logical memory error was about 1.43 × 10 ³ per cycle, and each increase of two in distance cut it by a factor of 2.14 [1]. Hold ⁻ Λ that factor fixed and the walk from 10 ³ to 10 ¹² takes about 28 increments, implying a distance ⁻ ⁻ near 63 and roughly 8,000 physical qubits per patch. Raise to ten and the same walk takes nine Λ increments, distance 25 and about 1,250 qubits per patch. A tenfold improvement in local error physics buys more than a sixfold reduction in area, which is why suppression per added qubit matters more than crossing threshold by a whisker. Google's 2026 result that reinforcement-learned calibration cuts logical error by about 20 percent during operation is a small step in exactly this direction [25].
Figure 1. Logical error per cycle against surface-code distance, starting from Google's measured distance-7 point. At today's suppression factor the Machine A target needs distance near 51 and the Machine B target sits beyond distance 63; at a suppression factor of ten both targets fall below distance 30. The vertical guides mark the physical footprint of a single logical patch.
Circuit failure compounds. When errors are rare and independent, failure probability is roughly the number of fault locations times the logical error per location. A computation with 10¹² locations at 10 ¹² error per location still fails about 63 percent of the time, because 1 minus e ¹ is ⁻ ⁻ 0.632. A ten percent failure budget needs average error near 10 ¹³. Retries therefore belong inside ⁻ every resource estimate, not in a footnote.
Decoding and latency. Every cycle produces syndrome data. Google's real-time decoder averaged 63 microseconds of latency on a distance-5 code cycling every 1.1 microseconds, keeping up by pipelining across up to a million cycles [1]. Averages are not enough at scale; large systems need parallel decoding with bounded tail latency, because non-Clifford operations and adaptive branches eventually need a decision before the next step. The ten-microsecond reaction time in modern factoring estimates is a control-architecture constraint pretending to be an algorithm parameter.
Rare events, leakage and drift. Threshold theorems assume local stochastic noise. Hardware produces cosmic-ray strikes, quasiparticle bursts, laser excursions, atom loss, leakage and calibration drift. Google reproduced correlated events about once per hour in repetition-code runs, roughly every three billion cycles [1]. Events like that impose an error floor that no amount of code distance removes. Leakage, meaning population outside the computational basis, can misbehave across several cycles; removing it costs time and qubits. Ignoring either understates both overhead and tail risk.
Magic-state economics. The Eastin-Knill theorem forbids a universal set of transversal logical gates in broad code classes, so most architectures inject magic states to execute T gates [48]. A factory takes noisy encoded states, performs Clifford operations and measurements, and emits fewer, cleaner states. Throughput must meet demand: an algorithm consuming 10¹¹ T states from one factory emitting 10,000 per second runs for 116 days; ten factories bring it to 11.6 days; a thousand bring it under three hours and may dominate the machine. Neutral atoms have demonstrated logical magic-state distillation [3]. That proves a mechanism, not industrial yield or continuous throughput.
Surface codes versus high-rate codes. Surface codes want only local two-dimensional connectivity and offer high thresholds, at the price of one logical qubit per d² physical. Quantum low-density parity-check codes encode many logical qubits at constant rate. IBM's [[144,12,12]] bivariate-bicycle memory uses 288 physical qubits, including checks, for 12 logical qubits at distance 12, or 24 physical per logical [15]. The ratio is compelling and incomplete: it requires nonlocal checks, reliable syndrome extraction, logical instructions, interfaces to processors and experimentally validated thresholds. A projected 24-to-1 memory is not a delivered 24-to-1 computer. Value it as a potential discontinuity, not as installed capacity.
6. Three machines you could actually build
The models below are engineering scenarios, not forecasts. They exist to expose dependencies. Costs cover hardware, facility and integration and exclude sunk research. Electricity is illustrative. Every assumption is stated so that a reader can change one and watch the answer move, and Table 2 collects them.
One caution applies to all three. Code distance is chosen here as a scenario parameter, not derived from a single formula, because the two anchors disagree. The textbook law with a one percent threshold says a 10 ¹ logical target at 10 ³ physical error needs only distance 17; Google's ⁻ ⁰ ⁻ measured of 2.14 says it needs distance near 51. The distances used below sit between those Λ anchors on purpose.
Machine A: an early fault-tolerant instrument. The workload uses 100 application logical qubits, 50 routing and ancilla qubits, 10 T gates, T-depth 10 and 10 Clifford-equivalent locations. ⁸ ⁷ ⁹ Physical error is 10 ³, the cycle is one microsecond, the failure budget is ten percent. At distance ⁻ 27 a patch needs about 1,457 core qubits; 300 logical-equivalent patches for data, routing, verification and one modest factory come to about 437,000 core qubits, and defects, spares, boundaries and controls raise the installed range to 0.5 to 1.0 million. At one clean T state per 100 cycles, a single factory needs about 1,000 seconds for 10 serial T layers; Clifford scheduling and ⁷ retries push wall time to roughly 0.5 to 4 hours. The facility draws 1 to 5 megawatts, most of it refrigeration, control and decoding rather than qubits. Delivered capex plausibly runs $200 million to $800 million. At 60 percent utilization, five-year depreciation and $50 million of annual operations, a machine-hour costs about $17,000 to $40,000 before margin. The first workloads must therefore create at least six-figure value per run. The binding constraint is not memory. It is stable integrated operation across half a million channels with a continuously available non-Clifford supply.
Machine B: a commercial scientific computer. The workload uses 1,000 application logical qubits, 500 routing and ancilla qubits, 10¹¹ T gates, T-depth 10 and about 10¹³ protected locations. ⁹ Physical error is 3 × 10 ⁴, the cycle one microsecond, the distance 31. Data and routing occupy ⁻ about 1,500 × 1,921, or about 2.9 million, core qubits; ten to a hundred factories plus links, spares and verification bring the installed count to 5 to 20 million. At 10 clean T states per second ⁶ aggregate, production alone takes about 28 hours, and scheduling and retries make it a one-to-seven-day job. Electrical demand is 10 to 30 megawatts and capex $1 billion to $5 billion. With 50 percent utilization, seven-year depreciation and $200 million to $700 million of annual operations, a dedicated machine-hour costs roughly $80,000 to $320,000. Customers can share memory but not oversubscribed factories or shared control bottlenecks. This machine is viable only for results worth millions to tens of millions each, or as sovereign scientific infrastructure. Its binding constraint is cost per verified result, not asymptotic complexity.
Machine C: a cryptographically relevant computer. This model adopts Gidney's 2025 estimate rather than force-fitting the generic one: 897,864 physical qubits before slack, a uniform 0.1 percent error assumption, one-microsecond surface-code cycles, ten-microsecond reaction time and about 4.96 days of expected runtime for RSA-2048 including retries [6]. At 5 to 20 megawatts, one run consumes 600 to 2,400 megawatt-hours, or $60,000 to $240,000 at $100 per megawatt-hour. Energy is not the cost. At $500 million to $2 billion capex, ten-year life, 50 percent availability and $100 million to $300 million of annual operations, a machine-hour is $34,000 to $114,000 and a dedicated five-day job costs about $4 million to $14 million before security, redundancy and margin. The strategic value of one successful attack can exceed that. The binding constraint is building the assumed reliable million-qubit system at all.
Table 2. Model sensitivities for the three machines. The last row names the assumption whose failure kills each model. Machine A: early FT Machine B: scientific Variable instrument computer Machine C: crypto machine Why it dominates Physical error 1.0 × 10⁻³ 3.0 × 10⁻⁴ 1.0 × 10⁻³ sets distance and retry burden Code distance 27 31 mixed, optimized patches drives qubit area and cycle latency Installed physical 0.5-1.0 M 5-20 M ~0.9-1.0 M manufacturing and control qubits scale Clean non-Clifford 10⁸ 10¹¹ algorithm-specific Toffolis sets factory area and runtime states Wall time per job 0.5-4 h 1-7 d ~5 d availability and customer value Electrical demand 1-5 MW 10-30 MW 5-20 MW facility and operating cost Capex $0.2-0.8 B $1-5 B $0.5-2 B financing and depreciation Cost per dedicated $17k-40k $80k-320k $34k-114k value each result must clear hour Principal kill unstable logical gates cost exceeds scientific correlated errors break the determines economic condition value estimate admission
7. The classical baseline moves
Quantum machines compete with a portfolio, not a laptop. CPUs bring serial control and vast software ecosystems. GPUs bring dense parallel arithmetic and memory bandwidth. AI accelerators bring cheap low-precision tensor operations. Supercomputers combine all three with networks and storage. ASICs trade flexibility for efficiency. And classical algorithms exploit problem structure with decades of engineering behind them.
Tensor networks compress quantum states when entanglement or circuit geometry allows it. Matrix-product states dominate one-dimensional and low-entanglement regimes; projected entangled-pair states, tree networks and clever contraction ordering extend the reach. A quantum device can generate states whose exact representation is exponential while the observables anyone cares about remain classically approximable.
Monte Carlo methods parallelize almost perfectly and come with confidence intervals. Their 1/ √N error law is what motivates amplitude estimation, but variance reduction, quasi-Monte Carlo, multilevel methods, control variates and learned surrogates keep moving the baseline. The fair comparison is optimized estimator against optimized estimator.
Classical optimization deploys branch-and-bound, cutting planes, relaxations, decomposition, heuristics and learned warm starts inside industrial solvers that have absorbed decades of tuning. A quantum heuristic must beat them on objective quality at equal time and hardware cost, on the customer's real constraints, not on a stripped Ising instance that discarded half of them.
In simulation, density-functional theory, coupled cluster, quantum Monte Carlo, tensor networks and embedding each own a region of chemistry. No single method covers everything, which is precisely why quantum advantage is most plausible where strong correlation defeats controlled classical approximation and the requested accuracy changes a material or catalyst decision. Meanwhile, AI accelerators improve the surrogate models that reduce how many expensive simulations anyone needs to run in the first place.
A complete comparison therefore adds up everything. Quantum time is compilation plus queueing plus calibration plus state preparation plus protected circuit time plus measurement plus repetitions plus decoding plus verification. Classical time is data preparation plus preprocessing plus solver time plus communication plus checkpointing plus verification. Both include capital and software. Both must normalize success probability, so that a quantum job succeeding 80 percent of the time is charged its retries against a classical job succeeding 99 percent of the time, and both must normalize output, because an approximate energy is not a certified bound and one sample is not a distribution. Verification may cost nearly as much as the baseline, and when a result is classically intractable, confidence has to come from structure: conserved quantities, bounds, cross-instance scaling, redundant algorithms, interactive proofs or experiment. Verification design is part of the product specification, not an afterthought.
8. Which workloads get through the door
The admission test below sorts workloads by the earliest machine that could produce economic evidence. "Useful now" means current systems provide a service customers value, not necessarily computational advantage. "Experimentally interesting" means the workload tests hardware or algorithms. "Fault-tolerant candidate" requires logical computation. "Probably unsuitable" means the structural taxes overwhelm the known speedup. Table 3 gives the verdicts; the paragraphs give the reasons. Appendix A works six of these cases in full.
Factoring and cryptanalysis. Compact input, compact output, verification by multiplication. Shor gives the cleanest asymptotic advantage in the field, and the compiled requirement sits near a million physical qubits for RSA-2048 under the aggressive 2025 design [6, 7]. Willingness to pay is strategic rather than commercial: intelligence and defence agencies may value a result enormously, while legitimate enterprises should migrate their cryptography rather than buy attacks [8]. Classification: fault-tolerant candidate with high strategic value and a tiny buyer set. Kill condition: post-quantum migration makes vulnerable targets irrelevant before the machine arrives. Symmetric cryptanalysis via Grover is weaker still, because doubling key lengths absorbs a quadratic speedup.
Quantum chemistry. Fault-tolerant phase estimation and qubitization offer controlled precision, and resource needs swing by orders of magnitude with basis, Hamiltonian factorization, initial-state overlap and error target [41, 42]. Small molecules stay classically easy. The valuable region is strongly correlated transition-metal chemistry where existing methods disagree and the answer changes a synthesis. Classification: leading fault-tolerant candidate. Earliest plausible machine: 50 to 1,000 high-quality logical qubits for selected active spaces, then larger machines for predictive industrial chemistry. Kill condition: classical embedding and learned potentials hit the required accuracy first, or quantum resource estimates stay above the value of the decision.
Materials and catalyst design. Materials add periodic structure, finite temperature, defects and phases, and the output has to connect to stability, conductivity, magnetism or kinetics. The 2024 catalyst-discovery benchmark developed for DARPA's Quantum Benchmarking program is the instructive case: it valued a high-utility calculation at about $200,000 and priced its conservative fault-tolerant execution at 139,000 QPU-hours, against about 400,000 CPU-hours for the classical DMRG alternative [9]. That is $1.44 of gross value per QPU-hour before data preparation, verification, depreciation or profit. Classification: fault-tolerant candidate with narrow early targets. Kill condition: no target carries decision value above complete quantum cost after realistic validation.
Drug discovery. Drug discovery is a workflow, not a problem. Target identification, docking, free-energy calculation, selectivity, toxicity, synthesis and trials have different bottlenecks, and a better electronic-structure kernel for one binding calculation does not raise clinical success. Verification requires experimental binding or synthesis, which takes weeks and costs more than compute. Classification: marketing claim as an end-to-end story; fault-tolerant candidate for selected chemistry kernels. Kill condition: quantum output uncertainty falls below model error yet the experimental hit rate does not move.
Combinatorial optimization and logistics. Annealing, QAOA, Grover variants and quantum walks apply to some formulations. Mapping introduces auxiliary variables, sparse hardware graphs require embedding, constraint penalties can exceed analogue precision, and variational training multiplies circuit evaluations. Customers care about improvement over the incumbent schedule within a fixed time, and the incumbent solver gets warm starts and domain rules [40]. Classification: experimentally interesting today; economically uncertain for annealing; probably unsuitable as a generic gate-model claim. Kill condition: a tuned classical solver matches objective quality, time and energy on held-out operational instances.
Portfolio optimization. The inputs, expected returns and covariances, are estimates with large statistical error, and the output is a trade list, not an optimum. Any advantage must exceed input uncertainty, market impact and turnover, and backtests are easy to overfit. Classification: marketing claim for broad advantage; experimental for constrained research instances.
Risk and Monte Carlo. Amplitude estimation offers a quadratic query improvement if the implementation can reversibly prepare paths, calculate payoffs and mark outcomes, all of which demand deep arithmetic and long coherence. Classification: fault-tolerant candidate where one sample is extremely expensive and moderate precision suffices. Kill condition: state-preparation cost or classical variance reduction removes the query advantage.
Machine learning. For classical data, loading is the central tax: amplitude-encoding N values can cost N operations without a quantum memory no one has built, and many exponential speedups assume oracle access the customer does not have. Dequantization has already converted several claimed exponential advantages into efficient classical algorithms under matched access. Classification: probably unsuitable for classical data; fault-tolerant candidate for quantum data from sensors, chemistry or another quantum processor. Kill condition: advantage disappears under matched model capacity, training budget and data access.
Linear algebra and differential equations. Quantum linear-system algorithms estimate properties of a solution state for sparse, well-conditioned systems and do not print the vector. If the customer needs every component, output cost destroys the exponential claim; if the customer needs one global observable, an advantage remains possible. Industrial PDE users usually need a field at many points with nonlinear boundary behaviour, and DARPA's benchmarking found economic advantage unclear for nonlinear differential equations [49]. Classification: fault-tolerant candidate under restrictive structure; marketing claim when presented generically.
Search. Grover is valuable when the search space is huge, the oracle is coherent and verification is cheap. Database search is unsuitable because indexed classical structures answer faster; cryptographic preimage search is structurally suitable but absorbed by longer keys. Classification: niche fault-tolerant candidate for expensive coherent oracles.
Quantum simulation. Digital and analogue simulation of many-body systems take Hamiltonians in and return local observables, correlation functions, spectra or phase diagrams. Analogue machines are useful scientific instruments now where they expose regimes hard to reach experimentally or classically, provided their claims survive calibration and cross-platform checks. Classification: useful now as research instrumentation; leading fault-tolerant candidate for economic advantage. Kill condition: no observable can be validated well enough to support a scientific decision.
Certified randomness and quantum-native sensing. Quantum devices can generate certified randomness and process quantum-native sensor outputs without classical conversion. These are real but small: useful now as specialized services, experimentally interesting for networks. Kill condition: classical or trusted-hardware alternatives deliver equivalent assurance at far lower cost.
Table 3. Workload admission summary. "FT" means a fault-tolerant machine; "data tax" is the cost of moving classical information in and out of the quantum state. Earliest plausible Workload Best quantum mechanism Data tax Verification class Economic verdict Factoring period finding low cheap large FT strategically decisive, narrow buyer set Chemistry phase estimation / medium bounds plus early to strongest commercial qubitization experiment commercial FT candidate Materials digital and analogue medium cross-method and analogue now; FT strong but target-specific simulation experiment later Drug discovery chemistry kernels high workflow tax wet lab commercial FT kernel value, not end-to- end claim Optimization annealing, QAOA, walks low-medium objective easy, current unproven general optimality hard experiments advantage Portfolio optimization / amplitude high statistical backtest FT weak admission estimation uncertainty Risk / Monte amplitude estimation high reversible state classical sampling commercial FT plausible where sampling is Carlo prep very costly Machine learning kernels, linear algebra often high held-out performance quantum-data weak for classical data first Linear algebra / quantum linear systems high unless oracle- observable checks / FT compact observables only PDEs native residuals Search amplitude amplification oracle-dependent cheap FT niche Quantum Hamiltonian simulation low-medium hard but structured analogue now; FT leading candidate simulation later
9. Verification is the product
A quantum computation is worth money only if the customer can trust the answer, and the difficulty of earning that trust ranges from trivial to existential. Factoring is easy: the answer is a short witness. Optimization allows objective evaluation but may not certify optimality. Sampling and many-body simulation can be classically intractable precisely where verification is hardest.
Verification comes in four flavours. Internal checks use conserved quantities, symmetries and code syndromes. Comparative checks run smaller instances and alternative methods. Interactive protocols let a classical verifier challenge a quantum prover. Physical checks compare predicted observables with experiment. High-value results need several of these at once when direct classical recomputation is unavailable.
Error bars must combine algorithmic approximation, finite sampling, logical faults, calibration drift and model error. A chemistry energy reported to microhartree precision is commercially misleading if the molecular model carries kilocalorie-per-mole uncertainty. Precision should be chosen backward from the decision threshold, not forward from what the machine can do.
Sampling cost surprises people. Estimating a probability near p to standard error takes roughly σ p(1 − p)/ shots. Error mitigation multiplies that. Postselection discards runs. Queue and reset σ time convert shot count into wall time. And vendor-reported fidelity is not a verification method. A customer contract should define the result, the confidence, the treatment of failure and who pays for reruns, and the verification protocol should exist before the workload runs, with acceptance thresholds and a classical fallback.
10. The complete economics
The unit that matters is cost per verified result. It equals allocated capital, energy, consumables, maintenance, calibration, software, cloud operations, failed runs, verification and customer integration, divided by accepted results.
Write annualized capex as C, annual operations as O, available hours as H, utilization as u and accepted-result yield as y. Base machine-hour cost is (C + O)/(H·u·y). A $1 billion system annualized at $150 million, with $150 million of operations, 8,760 hours, 60 percent utilization and 80 percent yield, costs about $71,000 per effective hour. A job needing 100 dedicated hours costs $7.1 million before margin. A $200,000 catalyst answer cannot carry that. A billion-dollar materials decision can, but only if the quantum result changes expected value rather than adding research prestige.
Utilization is not a given. Research systems lose time to calibration windows, queue fragmentation and customer-specific setup. A large job can reserve the whole machine while saturating only one resource, and factory congestion can leave data qubits idle. Pricing should allocate bottleneck capacity, not advertised qubits. Capex includes processors, refrigerators or vacuum plant, lasers, control racks, facility, networking and installation, and replacement cycles can be shorter than depreciation when each generation makes the last uncompetitive. Hardware companies face semiconductor-style reinvestment without semiconductor-style volume.
Willingness to pay. Customers pay for avoided cost, faster time, better yield, lower risk or strategic access, and scientific value is probabilistic: a better catalyst calculation matters only through fewer experiments or a better process. A workable pricing rule caps compute at 5 to 20 percent of expected customer value for uncertain exploratory results. A $10 million expected discovery benefit therefore supports $0.5 million to $2 million of compute, which at $71,000 per hour buys 7 to 28 hours on a mature shared machine, not days on a multibillion-dollar dedicated one.
The admission inequality. A workload is admitted when V × ΔP exceeds C + C + C − C, where
Q I V C
V is decision value, ΔP is the probability improvement attributable to the quantum result, C is
quantum compute cost, C integration cost, C verification cost and C the avoided classical cost.
I V C
The inequality kills a favourite error. A $100 billion market does not justify a $10 million calculation unless that calculation changes a decision with measurable probability. Total industry value is not value per result. The OECD's 2026 work on business readiness frames advantage the same way: a quantum workflow must be more efficient than the comparable classical one, end to end [39].
Who captures value. If hardware commoditizes, cloud aggregators, workflow owners, data holders and verification platforms gain bargaining power, and component suppliers keep value only where they control scarce lasers, detectors, cryogenic amplifiers or processes. If hardware stalls, component and control companies with adjacent markets survive best, application companies without classical products lose their platform, and public pure plays live on capital markets and government contracts. If fault tolerance arrives quickly, vertically integrated machine companies capture scarcity rents at first; over time algorithms and customer relationships matter more, and the best company may own a verified workflow and a procurement channel rather than the largest processor.
11. The industry map
The industry has six economic layers. Physics platforms build processors. Enabling hardware supplies refrigerators, vacuum, lasers, photonics and electronics. Fault-tolerance infrastructure provides decoders and control. Software compiles and orchestrates. Clouds distribute access. Applications integrate results into decisions. Each company below is placed by what it can defend and what would kill it.
Google Quantum AI builds superconducting transmons and holds the only distance-7 below-threshold memory with real-time decoding [1]. Its defensible assets are fabrication, control, algorithms and integration with hyperscale compute. Revenue is not separately disclosed. Kill condition: suppression factor and correlated-error floor fail to improve at larger distance.
IBM runs the largest superconducting cloud ecosystem, emphasizes circuit quality on Heron and Nighthawk, and has committed to Starling, a 200-logical-qubit, 100-million-gate qLDPC machine, in 2029 [14]. That is a roadmap, explicitly subject to change. Defensible assets are enterprise distribution, systems engineering, the compiler stack and patents. Kill condition: qLDPC checks, couplers and logical instructions fail at hardware scale.
Quantinuum listed on Nasdaq in June 2026, raising $1.68 billion at an implied valuation near $14 billion to $15 billion, with Honeywell retaining roughly half the votes [31]. Helios delivers peer-reviewed fidelity and scale, and the 2026 logical-error results are the strongest small-code evidence in the field [4, 5]. Defensible assets are ion transport, control, operation quality and full-stack software. Kill condition: logical operations per second remain too low for valuable circuits.
IonQ sells trapped-ion hardware, cloud access and systems, and has become an acquisition vehicle: it closed the $1.8 billion purchase of SkyWater Technology in July 2026 and has guided to $280 million to $290 million of 2026 revenue after $130.0 million in 2025. Its 2025 attributable net loss was $510.4 million, and its second-quarter 2026 GAAP loss of $1.87 billion was dominated by a non-cash warrant charge. Cash and investments stood near $3.0 billion mid-2026 [27]. Defensible assets are distribution, acquired capabilities and trapped-ion control. Kill condition: revenue growth remains procurement-and acquisition-led without application renewal.
Rigetti is a superconducting full stack with in-house fabrication, $7.1 million of 2025 revenue, an $84.7 million operating loss and about $590 million of cash [28]. Its defensible asset is iteration speed between fab and system. Kill condition: two-qubit quality and modular yield do not converge with leading systems.
QuEra combines neutral-atom analogue service with the fault-tolerant architecture demonstrated with Harvard and MIT. It announced $230 million of financing in 2025, part of it conditional, and was one of eleven companies advanced to DARPA's Stage B [33, 37]. Kill condition: loss-aware logical results fail under continuous customer operation. Atom Computing, with Microsoft, entangled 24 logical qubits on a 256-atom processor using a distance-two code that detects errors and corrects loss [23]. Kill condition: higher-distance repeated correction cannot preserve throughput.
Pasqal sells neutral-atom analogue access to European industrial and sovereign customers. Its risk is proving durable value beyond research and progressing to digital logical operation.
PsiQuantum raised $1 billion at a $7 billion valuation in 2025, signed a $125 million DARPA agreement in July 2026 and is building in Chicago and Queensland [34]. Its component results are peer reviewed; its principal risk is system yield across millions of components, especially loss. Kill condition: end-to-end detected-photon rate cannot support factory throughput.
Xanadu went public in March 2026, raising about $302 million [32]. Its assets are the Aurora modular photonic architecture and the widely adopted PennyLane framework. Kill condition: modular optical scale fails to cross fault-tolerance thresholds.
Alice & Bob pursues cat qubits with €130 million raised through early 2025 and a 2026 extension backed by NVIDIA's venture arm [35]. Kill condition: concatenated logical error remains near percent levels.
AWS explores bosonic codes with Ocelot and can absorb research cost while distributing eventual access through its cloud. Ocelot is a prototype, not a commercial logical processor [21].
Microsoft supplies Azure Quantum, resource estimation and orchestration, partners with Quantinuum and Atom Computing, and continues its topological bet. The platform is valuable independent of that bet. The hardware claim remains unverified at logical scale [22].
D-Wave leads annealing, is adding gate-model assets, and reported $24.6 million of 2025 revenue with $884.5 million of cash [29]. Its strength is a sold, accessible product and hybrid software. Kill condition: held-out operational benchmarks show no time, quality or cost advantage.
Quantum Computing Inc. ended 2025 with about $1.5 billion of cash and investments against $0.7 million of revenue and an adverse internal-control opinion [30]. Kill condition: capital converts into facilities without repeat product revenue.
Component suppliers are where the near-term margin lives. Bluefors and Oxford Instruments in dilution refrigeration; Qblox, Zurich Instruments and Quantum Machines in control; Keysight and Rohde & Schwarz in measurement; TOPTICA, M Squared and Menlo Systems in lasers; Single Quantum in detectors; GlobalFoundries and imec in fabrication. Every architecture consumes conventional components before any application advantage, and these businesses sell into sensing, communications and semiconductor markets too. The moat is performance, integration, service and qualification, not quantum branding.
Software companies such as Classiq, Q-CTRL, Riverlane and Quantum Machines, alongside NVIDIA's CUDA-Q, IBM's Qiskit, Google's Cirq and Xanadu's PennyLane, occupy overlapping layers. A software company needs one of three assets: proprietary error reduction with measured hardware gain, control of a customer workflow, or a neutral orchestration layer across scarce machines. Generic algorithm consulting is hard to defend, and cloud providers can bundle everything else.
Governments are funder, buyer, validator and regulator at once. DARPA's Quantum Benchmarking Initiative defines utility scale as computational value exceeding cost, has evaluated 20 companies, advanced 11 to Stage B in November 2025 and expects Stage C decisions in late 2026, with Microsoft and PsiQuantum on a parallel validation track [37]. The US Department of Energy committed $625 million to renew five national quantum centres in November 2025 and launched a Quantum Genesis initiative in June 2026 targeting fault-tolerant systems with low hundreds of logical qubits by 2028 [36]. The National Quantum Initiative reauthorization has cleared committees in both chambers and, as of this writing, has not been enacted. The European Quantum Flagship runs €1 billion over ten years [38]. Public money is rational where spillovers, security and infrastructure exceed private capture. It can also mask weak product economics, so analysis should separate competitively awarded research, system procurement, reimbursed milestones and recurring commercial demand.
Table 4. Public-company financial reality. Fiscal 2025 figures from filed reports; 2026 items as noted. Market capitalizations are excluded because they change daily and measure sentiment, not delivery. Sources: company filings and releases [27-32, 50]. Company revenue 2025 loss Liquidity 2026 developments Reading IonQ $130.0 M $510.4 M attributable net ~$3.0 B mid- SkyWater acquired ($1.8 B); scale and acquisitions funded; loss 2026 FY26 guide $280-290 M compute economics unproven Quantinuum not disclosed not disclosed $1.68 B Nasdaq listing June 2026; strongest fidelity evidence; pre-IPO raised at IPO Helios in Nature throughput is the question D-Wave $24.6 M $355.1 M net loss, incl. $884.5 M Advantage2 general best annealing product $270.5 M non-cash warrant availability evidence, still early charge Rigetti $7.1 M $84.7 M operating loss ~$590 M none material research-scale revenue, dilution-sensitive Xanadu not disclosed not disclosed ~$302 M Nasdaq listing March 2026 photonics option with software pre-IPO raised at IPO franchise Quantum $0.7 M $18.7 M net loss ~$1.5 B Luminar Semiconductor financing capacity far exceeds Computing Inc. acquired ($110 M) demonstrated demand
12. Investment architecture
Investors can own component revenue, machine scarcity, platform distribution, application workflows or research optionality. These are different securities in economic substance even when every one of them carries the quantum label.
Component companies sell refrigerators, lasers, detectors, electronics, packaging and fabrication. The revenue unit is hardware, service or qualified capacity; gross margin depends on specialization and volume; capital intensity is familiar; and quantum failure does not erase adjacent demand. Machine companies sell cloud time, subscriptions, dedicated systems, government milestones and partnerships. Their gross margin is obscured by R&D, low utilization and rapid obsolescence, customer concentration is high, and revenue may represent prototype delivery rather than recurring computation. Platforms sell workflow access and orchestration, hyperscalers can subsidize the layer to pull broader cloud use, and switching costs arise from integration and validation rather than circuit syntax. Application companies sell a business result and should charge per decision, design, schedule or risk report. The best of them are quantum-ready but classically useful. A company that cannot create value before fault tolerance is a financed waiting room.
The capital sequence. Research capital funds physical mechanisms and prototypes. Venture capital funds repeatable subsystems and teams. Growth capital funds manufacturing lines and distribution. Infrastructure capital funds stable, contracted machines. Project finance requires predictable uptime, customers and residual value. Quantum companies routinely request growth capital while still carrying research risk, and the mismatch shows up as dilution. Each capital class should be unlocked by evidence: repeated fabrication, serviceable modules, logical throughput, contracted capacity, uptime and gross margin. The 2026 IPO wave, four quantum listings in six months, moved a great deal of research risk onto public balance sheets ahead of that evidence [31, 32].
What is investable now. Most attractive: scarce enabling components with adjacent demand; leading private hardware teams after independently verified milestones; and public platforms whose quantum program is an inexpensive option inside a larger business. Selective exposure to pure plays can be justified as a portfolio of technical options, sized for binary risk, dilution and long duration, and never on revenue multiples when current revenue is government-funded engineering and terminal value depends on a different product. Least attractive: application shells without proprietary data, hardware access or classical revenue; companies using announced qubits as capacity; and forecasts that multiply a large end market by an arbitrary quantum share.
13. Ten theses, each with a falsifier
A thesis that cannot be killed is a slogan. Each of the ten below names the observation that would refute it.
1. Logical work is the only output that matters. Physical qubits become valuable only through reliable logical operations. Track logical qubits, error per logical operation, supported gate set, depth, throughput and uptime. Falsifier: a physical-qubit metric repeatedly predicts verified workload value better than logical measures do. 2. Codes, decoders and factories set the machine's size. Hardware that cannot expose these mechanisms has no credible path to scale. Falsifier: a broadly useful workload wins economically on uncorrected hardware with stable repeat demand.
3. Verification belongs in the quote. A result without a trust mechanism is a research signal, not a purchasable answer. Falsifier: customers repeatedly buy intractable outputs without independent confidence and suffer no adverse selection.
4. Speedups follow mathematical structure, not industry labels. Chemistry, logistics and finance each contain admitted and rejected tasks. Falsifier: one hardware benchmark predicts broad advantage across unrelated workloads.
5. The classical baseline keeps learning. Tensor networks, GPUs, solvers and AI surrogates improve during quantum development, and resource estimates must include their learning curve. Falsifier: classical performance plateaus across the relevant workloads for several generations.
6. Components monetize first. Every modality needs precision electronics, calibration, lasers, cryogenics or vacuum, sold before application advantage and often into adjacent markets. Falsifier: integrated builders internalize the stack at lower cost and external component revenue stalls.
7. Yield is the blueprint's truth test. A million-qubit design is worthless if module yield compounds toward zero, so publish wafer statistics, component distributions, assembly yield and field replacement. Falsifier: one-off tuning remains sufficient at commercial scale.
8. Quantum processors are accelerators inside classical systems. Scheduling, preprocessing, decoding and verification set effective throughput. Falsifier: customers run economically valuable workloads end to end without classical orchestration.
9. Admission is an inequality, not a market-size argument. Value times attributable probability improvement must exceed quantum, integration and verification costs net of avoided classical cost. Falsifier: quantum services sustain profitable demand while routinely costing more than the value they create.
0. The processor may not be where the money ends up. Distribution, components, workflow data, verification and manufacturing can capture more value than processor ownership. Falsifier: market rents remain permanently concentrated in the highest-qubit hardware provider.
Behind the ten sits one causal chain, and it is multiplicative. Physics determines error channels and gate mechanisms. Engineering determines whether those mechanisms survive packaging, wiring and drift. Software determines whether logical resources map efficiently. Markets determine which outputs matter. Institutions fund long horizons and set security requirements. Capital determines how many redesign cycles survive. A good qubit with poor yield fails. A high-yield chip with an overwhelmed decoder fails. A reliable logical machine with no admitted workload fails commercially. An important workload without verification fails as a product. Logical capacity without manufacturing is a laboratory; manufacturing without workloads is stranded capex; workload promises without logical capacity are consulting. Commercial scale begins where all three curves reinforce one another, and that pattern, not the calendar, should set capital timing.
14. Four scenarios, triggered by evidence
Scenarios here are triggered by measurements, not dates. The calendar windows indicate when evidence could plausibly accumulate and overlap on purpose; two of them describe the same years unfolding at different speeds.
Scenario A: progress stalls before useful error correction. Trigger: logical suppression stays below a factor of three per distance increment; correlated floors persist above 10; logical gates ⁻ ⁹ fail to scale beyond small codes. Plausible window: 2026 to 2032. Machines remain research instruments. Winning workloads are analogue science, education, randomness and subsidized pilots; winning companies are components, control, cryogenics, lasers and diversified clouds. Hardware equity returns depend on strategic acquisition rather than compute margin. Falsifier: a system runs more than 10 non-Clifford logical operations with stable uptime and independent ⁶ verification.
Scenario B: narrow scientific advantage emerges. Trigger: 50 to 200 logical qubits execute deep phase-estimation or simulation circuits with accepted results. Plausible window: 2028 to 2035. Required machine: 0.5 to 5 million physical qubits or a lower-overhead equivalent, hours of uptime and credible verification. Winning workloads are quantum dynamics, strongly correlated active spaces and specialized materials; customers are governments, national laboratories and high-value chemical firms; capital requirement is hundreds of millions to low billions. Falsifier: classical methods reproduce the results at lower complete cost within a year.
Scenario C: broad fault-tolerant utility develops slowly. Trigger: hundreds to thousands of logical qubits, 10 to 10¹¹ reliable non-Clifford operations, multi-day uptime and several paying ⁸ workflows. Plausible window: 2032 to 2042. Systems cost billions and run through clouds or sovereign centres. Winners combine hardware, orchestration and customer access; chemistry, materials, risk and selected search become viable. Falsifier: unit economics fail to improve with each generation, or utilization stays subsidy-driven.
Scenario D: large-scale fault tolerance arrives fast. Trigger: high-rate codes work experimentally, modular links exceed required fidelity, factories run continuously at high yield and manufacturing scales by orders of magnitude. Plausible window: 2028 to 2035, the same years as Scenario B, compressed. Machines offer thousands of logical qubits and trillions of protected operations; cryptanalysis, broad simulation and some Monte Carlo become urgent; post-quantum migration accelerates; hardware scarcity produces high margins and infrastructure finance appears once capacity is contracted. Falsifier: any one of code, link, factory or yield fails at module scale.
15. Kill conditions and verdict
The thesis must be killable, so here is what kills it. Technically: failure of logical suppression, correlated-error floors, unscalable control power, poor fabrication yield, insufficient decoder speed, factory bottlenecks, module-link loss and unverifiable outputs. Commercially: classical cost falling faster, customers refusing workflow change, result value below compute cost, procurement concentrated in subsidies, low utilization, service margins consumed by calibration and private capital unavailable for the next generation. Appendix B turns these into a diligence checklist.
The positive thesis survives today because several independent modalities have demonstrated pieces of fault tolerance, algorithms keep lowering resource needs, and governments are funding rigorous validation. It remains conditional because no company has integrated those pieces into a profitable verified-result machine, and because the 2026 IPO wave has priced in a good deal of integration that has not happened yet.
The central answer is therefore precise. Quantum computers can do things classical computers are not expected to do economically when the task exposes exploitable quantum structure, the output is compact, the input avoids large classical loading, the calculation can be made fault tolerant at tolerable cost and verification is cheaper than recomputation. The leading candidates are cryptanalysis, quantum simulation and selected chemistry. Monte Carlo and structured linear algebra remain conditional. Generic optimization, portfolio selection and classical-data machine learning do not presently pass.
For investors, the posture is neither dismissal nor enthusiasm. Keep exposure to scarce capabilities, insist on complete-machine arithmetic, fund falsifiable milestones, hold infrastructure capital for repeatability and treat every workload as its own admission decision. For founders, sell evidence and accepted outcomes. For engineers, optimize the protected workflow rather than the qubit. For policymakers, fund independent validation, standards, workforce and security migration, and keep termination rights.
The investable signal is not the next qubit announcement. It is the first repeated contract for verified results, supported by falling physical resources per logical operation, rising factory throughput, disclosed uptime and a customer who renews. Until that appears, quantum computing is a strategic industrial buildout with valuable components and real scientific progress, and only embryonic compute economics. Count verified logical work, complete cost and repeat customers. Everything else is an input, a projection, or a scientific milestone whose economic meaning still has to be proved.
Appendix A. Six worked cases
Each case runs one workload through the same seven questions: the decision it serves, its input and output, the quantum method, the complete machine it needs, the classical baseline, verification and value, and the verdict with its kill conditions.
A1. RSA-2048 factoring Decision. The operational question is not whether Shor's algorithm has asymptotic advantage; it does. It is when a real machine can factor a 2048-bit modulus in useful time, and whether that possibility changes security decisions today. For a defender it already does, because sensitive ciphertext may stay valuable for decades and cryptographic migration is slow.
Input and output. A compact public modulus in; two prime factors out, checked by one multiplication. Loading and verification could not be more favourable.
Method. Shor reduces factoring to order finding and phase estimation with extensive reversible modular arithmetic. The compiled circuit is heavy in non-Clifford operations and needs reliable feed-forward. Improvements in arithmetic, windowing, lattice surgery and magic-state scheduling have cut estimated resources by more than twentyfold since 2021 [6, 7].
Complete machine. Gidney's 2025 estimate places the job below a million noisy qubits and one week under 0.1 percent physical error, one-microsecond cycles and ten-microsecond reaction time. Those values must coexist. Slower feedback, higher error, limited connectivity or weak factory throughput enlarges the system or the runtime. A blueprint is not a delivered machine [6].
Classical baseline. No known classical algorithm factors RSA-2048 economically, and specialized hardware does not close the gap. The baseline is unusually stable.
Verification and value. Verification is trivial. Value is asymmetric: offensive value can be enormous but lawful use is restricted, while defensive value comes from migrating before exposure. Investable revenue accrues to post-quantum migration, key inventory, hardware security modules and assurance well before any factoring service exists.
Verdict. Algorithm and verification gates pass. Hardware, cost and lawful payment gates fail today. The commercial action is defensive migration, not buying factoring capacity. Kill conditions: for defenders, none, because store-now-decrypt-later exposure does not depend on the machine's arrival date; for an offensive-compute thesis, physical cost staying above sovereign willingness to pay once error-corrected modules are measured.
A2. Ground-state energies for catalytic chemistry Decision. A chemical company wants an energy difference or reaction mechanism precise enough to select candidates and cut laboratory cycles. Value is high if the result changes a synthesis, catalyst or process decision, and near zero if experimental uncertainty, solvent effects or kinetics dominate.
Input and output. Electronic-structure Hamiltonians are structured, so loading is favourable, and the output is a compact energy. But building the active space, integrals and effective Hamiltonian is substantial classical work.
Method. Fault-tolerant phase estimation with qubitization is the clearest path to systematic precision. State preparation is the central uncertainty: low overlap between the initial state and the target eigenstate means repetition or elaborate preparation that erodes the advantage.
Complete machine. Resources depend on active-space size, precision, Hamiltonian representation, physical error, code and factories. Tensor hypercontraction and better arithmetic reduce T counts [41], yet useful instances may still need hundreds to thousands of logical qubits and very large protected depth. A 25-logical-qubit demonstration can be scientifically valuable without touching the industrial target.
Classical baseline. Coupled cluster, DMRG, selected configuration interaction, quantum Monte Carlo, density-functional theory and learned potentials form a portfolio whose best member changes with the molecule. Domain experts must optimize it independently.
Verification and value. Small active spaces can be checked classically. Larger outputs use convergence tests, symmetry, multiple ansätze, cross-platform runs and, eventually, experiment, which can take months and confounds attribution.
Verdict. Structured input and compact output pass; algorithmic relevance is strong; hardware, verification cost and willingness to pay are conditional. The catalyst benchmark's $1.44 per QPU-hour shows the value-density gap under conservative resources. A viable target must carry far larger decision value or need far less quantum space-time. Kill conditions: classical embedding and tensor methods keep accepted error below the customer's threshold at lower cost; or state preparation and factory demand dominate after every algorithmic reduction.
A3. Quantum dynamics and new materials Decision. The customer wants a spectral property, transport coefficient or dynamical response of a strongly correlated material that classical approximations cannot resolve, and the result must change material selection, device design or scientific interpretation.
Input and output. Lattice Hamiltonians and local interactions are compact; so are correlation functions and spectra, though resolving fine features requires long evolution and many samples. Mapping a real material onto an effective model can introduce more error than the solver.
Method. Hamiltonian simulation, phase estimation and response-function algorithms exploit quantum evolution directly. Analogue simulators reach interesting regimes sooner with weaker programmability and verification.
Complete machine. Logical width may be moderate for reduced models, while depth and sampling can be large. Analogue platforms must still budget control error, finite temperature and mapping fidelity.
Classical baseline. Tensor networks are formidable in one dimension and low-entanglement regimes; quantum Monte Carlo excels without sign problems; dynamical mean-field theory, exact diagonalization, embedding and surrogates cover other regions. An instance is attractive only where the comparator's failure mechanism is understood.
Verification and value. Check solvable limits, conservation laws, sum rules, short-time series, cross-platform results and experimental spectra. Verification stays cheaper when it targets a few observables rather than reconstructing the state.
Verdict. A credible early scientific category, because quantum structure is native and outputs are compact. Economic admission remains narrow; national laboratories and high-value materials programs are the plausible buyers. Kill conditions: classical tensor and embedding methods expand into all valuable regimes; experimental noise exceeds the computational improvement; or verification requires full classical simulation.
A4. Monte Carlo and risk estimation Decision. A financial, logistics or energy firm estimates an expected loss, tail probability or price under a stochastic model. A faster estimate has value only if it changes a time-sensitive decision, capital allocation or service level.
Input and output. Output is compact. Input is the problem: amplitude estimation needs coherent preparation of a probability distribution and reversible evaluation of the payoff, and production models with branching logic, calibration data and path dependence make those oracles expensive.
Method. Ideal amplitude estimation cuts oracle calls quadratically with respect to sampling error. Practical variants trade coherence for repetitions. Fault-tolerant arithmetic, function approximation and controlled state preparation set the constants.
Complete machine. Hundreds to thousands of logical qubits after registers and arithmetic; high depth because each round calls the full model coherently; factories sustaining arithmetic; logical reaction time and parallel classical competition setting the wall-clock benefit.
Classical baseline. GPUs, quasi-Monte Carlo, multilevel methods, variance reduction, adjoints and surrogates cut sample costs dramatically, parallelize easily and use mature data pipelines. The baseline is the production implementation, not textbook Monte Carlo.
Verification and value. Statistical confidence is native, so outputs test easily on held-out cases, though verifying a small error advantage may itself need many samples. Regulated models also require interpretability, lineage and change control.
Verdict. The algorithmic gate passes in an oracle model. Data loading, reversible implementation, full-depth hardware and economics remain conditional. A strong target has expensive paths, compact structured state preparation, weak classical variance reduction and high value per second. Kill conditions: classical variance reduction offsets the query advantage; oracle construction consumes most protected gates; or elastic accelerators meet the latency requirement cheaper.
A5. Combinatorial optimization Decision. A better schedule, route, portfolio or allocation under time and policy constraints. Value comes from beating the production incumbent, not from reaching a mathematical optimum on a toy formulation.
Input and output. Inputs are classical and compact; outputs are candidate solutions that are easy to score. The hard part is encoding every constraint, stochastic condition and business rule without destroying structure.
Method. Annealing, QAOA, quantum walks, Grover-style search and hybrid decomposition. Rigorous speedups exist for some oracle models; consistent practical advantage on production distributions has not been shown.
Complete machine. Near-term methods need many evaluations and sensitive parameter tuning. Fault-tolerant search needs deep coherent oracles for at most quadratic generic improvement. Annealer embedding can spend many physical qubits per logical variable and distort precision.
Classical baseline. Mixed-integer solvers, constraint programming, local search, decomposition, specialized heuristics and learned policies, all exploiting business structure and warm starts, with human-designed operating rules and equal engineering effort included.
Verification and value. Candidate quality is easy to compute. Proving superiority over all reasonable classical alternatives is hard. A one percent improvement is valuable in one operation and irrelevant in another.
Verdict. Verification and compact output pass; algorithmic and comparative gates generally fail today. Treat this as a benchmark market with possible narrow wins, not the default first application. Kill conditions: held-out customer instances show no reliable advantage after equal tuning, or encoding and decomposition remain bespoke. A decisive positive result would be repeated improvement on live distributions at lower complete time or cost.
A6. Machine learning on classical data Decision. Better prediction, generation or optimization from a large classical dataset, measured against continuously improving classical models and accelerators.
Input and output. Loading classical data is often fatal to theoretical speedups, because efficient amplitude encoding assumes a data-access mechanism whose construction and update cost can dominate. Large classical outputs create the same problem in reverse.
Method. Kernel estimation, variational circuits, linear-system subroutines and quantum generative models. Some show mathematical separations under data and oracle assumptions; generalization, noise and trainability are open research. Complete machine. Useful models may need fault-tolerant arithmetic, coherent memory access and repeated training. Near-term variational methods use shallow circuits but face sampling overhead, barren plateaus, noise and classical optimization loops.
Classical baseline. Extraordinary hardware scale, algorithmic investment, software maturity and pretrained models, with approximate answers acceptable in most business settings. This is the fastest-moving baseline in the paper.
Verification and value. Held-out prediction quality is easy to measure. Attribution is hard, because data cleaning, feature engineering and classical components can explain gains. A fair trial freezes datasets, budgets and hyperparameter effort.
Verdict. Generic classical-data learning fails the present test. Narrow cases involving quantum-generated data, quantum states or sampling from physically native distributions may pass earlier because they avoid loading. Kill conditions: input and output overhead erase circuit gains, or classical foundation models outrun quantum capacity. The thesis becomes credible only after a held-out production task shows reproducible quality or cost benefit against a fully optimized classical stack.
A7. The six cases side by side RSA factoring has the strongest algorithm and the cheapest verification, the most distant hardware and the most restricted market. Chemistry and materials have native quantum structure and potentially high value, with state preparation, model error and classical competition varying by instance. Monte Carlo has a clean quadratic theorem and expensive coherent oracles. Optimization has easy scoring and the harshest heuristic baseline. Classical-data machine learning combines costly loading with the fastest classical progress. An investor should therefore avoid a single "applications" exposure: pair fault-tolerant chemistry or materials tools with classical baseline expertise, verification software and domain distribution; capture cryptographic exposure through migration and assurance; and fund optimization and machine-learning claims as milestone experiments with explicit held-out tests.
Appendix B. Method and diligence checklist
B1. Units and accounting boundary The paper uses five nested units. A physical operation is a pulse, transport, measurement or reset on a device. A correction cycle is one complete syndrome-extraction round. A logical operation acts on protected information and includes the correction that supports it. A job is one attempt at an algorithmic circuit, including shots and branches. An accepted result is a job, or set of jobs, that passes a pre-agreed correctness and confidence test.
Comparisons use accepted results wherever possible. That boundary charges unsuccessful shots, calibration, compilation, queueing, decoding, classical preprocessing, verification and allocated facility cost. It credits avoided classical computation. It does not credit vague option value unless the purchaser assigns it a cash value and can explain attribution.
B2. Logical-error and factory models
(d+1)/2
Below threshold, the paper uses p = A (p/p ) as an interpolation tool, with A and p
L th th
architecture-specific. Required distance follows from the number of error opportunities: a circuit exposing N logical locations under a total failure budget needs p below /N on a first pass, ε ε
before margins for correlations, leakage, factories and logical gates. This is why a logical memory rate cannot be copied into an application estimate, and why Section 6 treats distance as a scenario parameter bracketed by the textbook law and the measured suppression factor.
Let R be the peak non-Clifford consumption rate after compilation and R the
consume factory
accepted output per factory after distillation failure, quality testing and transport. Required factories equal the ceiling of R /R times a redundancy factor. Factory area is count
consume factory
times physical qubits per factory plus routing; latency is the greater of data-path depth and factory-constrained time. Any resource estimate that omits peak demand, accepted yield or transport is flagged, because bursty circuits can idle an expensive data block even when average T count looks fine.
B3. Cost per accepted result Annualized system cost is depreciation or required capital return plus labour, facility, energy, consumables, service, software and allocated overhead. Sellable capacity is calendar time times hardware availability times calibrated availability times scheduling efficiency times paid utilization. Cost per sellable second is the ratio. Job cost is sellable-second cost times quantum duration plus variable consumables, preprocessing, compilation, data movement, decoding, sampling, retries and verification. Cost per accepted result divides expected job cost by acceptance probability, and provider-funded retries are a cost, never revenue.
B4. The admission inequality and the baseline protocol A workload is admitted when attributable expected value plus avoided classical cost exceeds quantum workflow cost, integration cost, verification cost and risk-adjusted switching cost. Attributable expected value is the economic consequence of a decision times the probability that the quantum result changes that decision and improves the outcome. The inequality rejects high-value industries when the result is not decision-relevant and admits modest computations that repeat often, verify cheaply and deliver at high margin.
The comparator team receives the same input, output tolerance and wall-clock definition and may use reformulation, symmetry, approximation, accelerators, distributed computing, tensor networks, Monte Carlo, surrogates and domain heuristics, with development time treated symmetrically. The baseline is frozen only for the duration of a controlled benchmark and then updated for investment planning. Advantage requires a statistically defensible difference after total cost and accuracy are matched. Utility may exist without asymptotic advantage if the result creates value unavailable within the customer's time window. Supremacy is a computational separation and carries no economic conclusion.
B5. Confidence classes and financial normalization Measured, independently replicated evidence receives the highest weight. Measured vendor evidence without replication receives high but conditional weight. Peer-reviewed projections and transparent resource estimates receive medium weight. Roadmaps, investor presentations and simulation-only architecture claims receive low predictive weight, though they identify intended designs. Relevance matters as much as quality: a precise single-qubit measurement is strong evidence about that component and weak evidence about full-system economics.
Company financials use fiscal 2025 filings and 2026 interim reports. Cash includes unrestricted cash, equivalents and marketable investments and excludes undrawn facilities. Runway is not quoted as a single number where acquisitions, facility commitments or volatile securities make it misleading. Valuation is deliberately not presented as a point target; the appropriate approach is scenario-weighted enterprise value with explicit dilution, capital needs and terminal outcomes.
B6. Twenty decisive experiments The field would move fastest if these were run and published. Run the same universal logical circuit family at increasing distance and show decreasing computation-level failure, not just memory error. Operate a logical register for an application-equivalent number of cycles and publish every rare event. Decode in real time at projected full-system syndrome bandwidth with measured energy and 99.999th-percentile latency. Run logical Clifford and non-Clifford gates concurrently with syndrome extraction across multiple blocks. Produce magic states for days, route them into data blocks and measure accepted throughput and contamination. Scale factory count and confirm throughput rises without data-block fidelity collapsing. Demonstrate logical entanglement across modules at application rate. Remove a physical component mid-
computation and remap around it. Fabricate multiple lots and publish the distribution of accepted modules. Commission two nominally identical systems and reproduce logical performance within a declared tolerance. Run full-width simultaneous operations and compare error correlations with isolated benchmarks. Recover automatically from deliberate calibration drift within a bounded time. Reproduce a claimed advantage on an independent quantum system with the same acceptance test. Give independent classical teams a year to optimize the comparator before locking a benchmark. Complete a chemistry or materials calculation later confirmed experimentally that changes a real development decision. Show a compact output whose verification cost grows materially slower than classical solution cost. Sell an accepted-result contract with provider-paid reruns and report positive contribution margin. Renew that customer at greater volume without grant funding. Operate a system for a year and publish calibrated availability, incidents, repair time and billable utilization. Show three successive generations with declining inflation-adjusted cost per accepted logical operation.
B7. Diligence checklist Hardware. Request the full distribution of one-and two-qubit performance across every active device, not the median or the champion pair, and recompute simultaneous circuit yield from the tails. Reconcile the public qubit count to fabricated, packaged, connected, calibrated, active, algorithmic and logical qubits. Examine time-stamped performance over at least a quarter to separate new hardware from device selection and calibration effort. Inspect raw syndrome data for temporal and spatial correlation; treat independent-error fits as optimistic until rare events are disclosed. Repeat benchmarks with simultaneous operations across the widest usable region. Measure reset, measurement, leakage and idling under the exact correction schedule. Ask which mechanism sets the present error floor and what experiment would prove that diagnosis wrong. Require a distance series on multiple devices or lots. Separate logical memory performance from logical gate performance. Audit decoder hardware and latency tails at projected syndrome volume. Map every cable, fibre and feedthrough in the scale-up plan and find the first density or heat-load limit. Review wall-plug-to-qubit energy. Obtain wafer, die, package and module yield by lot. Inspect failure containment: does one dead qubit, laser or control card stop a job, a region or the machine? Measure mean time to diagnose and repair, including warm-up, cooldown and realignment. For modular systems demand a joint curve of fidelity, rate, loss and memory wait. For photonics multiply source, coupling, switching, interference and detection probabilities through the full path. For atoms and ions account for loss, reload, transport and motional heating under long schedules. For bosonic systems evaluate both error channels plus bias-preserving universal gates. End with one falsifiable twelve-month integration milestone that combines width, depth, correction and availability.
Algorithm and workload. Write the customer decision before choosing an algorithm. Define input size, structure, precision and update frequency, and cost every loading step. Define the smallest output that creates value and reject plans that require reading a state or a large vector. State the mathematical source of speedup and every promise it assumes, then test production data against those promises. Compile to an explicit logical gate set and report width, depth, non-Clifford count, measurements, branches and peak factory demand. Allocate a total failure budget across gates, factories, memory, measurement, state preparation and verification. Model at least two correction architectures. Include routing and layout. Include sampling and confidence, with mitigation's effect on shot count. Benchmark state preparation separately. Appoint an independent classical team with equal time and full freedom to reformulate. Freeze an acceptance test before running the comparison. Test a scaling family, not one instance. Re-run the classical search after the quantum result is public. Separate scientific novelty from economic value. Require a verification protocol with cost scaling. Measure robustness to model uncertainty. Identify the customer's next-best action without the quantum result. Quantify integration labour and data governance. Conclude with pass, conditional or fail on each of the five gates.
Commercial. Reconcile revenue to hardware sales, access, research contracts, consulting, grants and pass-through procurement, and assign each its own recurrence and margin. Examine the five largest customers, their funding source and termination rights. Request renewal, expansion and churn by workload. Identify the contractual unit and who bears calibration and retry risk. Rebuild gross margin with complete service labour, cloud fees, depreciation, support and verification. Calculate sellable utilization after maintenance, calibration, queue fragmentation and research reservations. Compare price with the customer's maximum attributable decision value. Examine sales-cycle length, security review, data localization and integration milestones. Test whether the product works without the founding scientific team. Inspect backlog definitions and cancellation clauses. Map customer concentration by sector and sovereign funding source. Determine who owns the customer, the usage data and the application layer. Evaluate intellectual property by freedom to operate and manufacturing know-how, not patent count. Model the price declines needed for market expansion. Identify adjacent revenue that survives a ten-year delay. Assess supplier concentration and lead times. Determine which claims need export licences. Review liability, warranty and acceptance language. Interview customers who declined or abandoned pilots. End with a renewal milestone tied to a named workload, an accepted-result unit and positive contribution margin.
Financial and governance. Reconcile unrestricted cash, investments, restricted balances, debt, warrants and acquisition obligations to audited filings. Build cash burn from operating cash flow plus capex and committed facilities, since accounting loss is distorted by non-cash financing items, as the 2025 and 2026 results of several public companies show. Match runway to the cash required for the next falsifiable milestone. Model dilution from options, warrants, convertibles and at-the-market programs. Separate research equipment from repeatable production assets. Estimate commissioning time from purchase order to billable operation. Stress facility cost for power, cooling, vibration, cleanroom, vacuum and security. Review revenue recognition for milestone contracts. Inspect related-party transactions and strategic investor rights. Compare stock-based with cash compensation. Evaluate acquisition accounting and integration risk. Review internal-control findings. Map board expertise across physics, manufacturing, systems, security, capital projects and customer industries. Test whether executive incentives reward
logical performance and recurring margin or promotional qubit and booking targets. Track disclosure changes over time. Compare actual milestones with prior schedules and use the delay distribution to adjust roadmap probabilities. Model downside liquidation value. Identify capital providers for each scenario. Treat government awards as staged options. Approve capital in tranches tied to independent evidence.
B8. Limits of this paper Public data underdescribe fleet distributions, yield, uptime, calibration labour, system cost and customer renewal. Several 2025 and 2026 results are preprints or vendor releases, and some peer-reviewed demonstrations use selected devices and conditional metrics. The paper labels these distinctions but cannot reconstruct private raw data. The scenarios are decision frameworks rather than forecasts, and any investment decision should refresh financial statements, financing terms, technical results and classical baselines at the time of execution. Nothing here is investment, legal or security advice.
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