Quantum Capability Has Doubled Every One to Two Years. Sandia Says the Early-2030s Roadmaps Need Four Times That.

Sep 10, 2026 – A team led by Sandia National Laboratories’ Quantum Performance Laboratory published a cross-platform measurement of quantum computational capability, benchmarking processors from Google, IBM and Quantinuum with a single test and applying that same test to a fault-tolerant processor running on logical qubits. The authors describe it as the first experiment to compare physical- and logical-qubit computation on an identical footing.

The 46-page preprint, arXiv:2609.12146, introduces the quantum universal operation performance system, or QUOPS. Timothy Proctor of Sandia’s Livermore laboratory is first author and Robin Blume-Kohout of Sandia’s Albuquerque laboratory is senior author, on a paper with 30 authors drawn from Sandia, Quantinuum’s sites in Cambridge, Oxford and Broomfield, NVIDIA and the University of New Mexico. Sandia posted the preprint three days before IEEE Quantum Week opened in Toronto.

A QUOPS circuit alternates layers of randomly chosen single-qubit Pauli rotations with layers of CNOT gates. The benchmark runs those circuits at many combinations of width and size, records which combinations the machine executes successfully, and reports two numbers: a QUOPS score, the largest circuit size the machine completes inside a defined region of shapes, and a QUOPS rate, an effective throughput that folds in wall-clock time, mirror-circuit overhead, measured polarization and discarded shots.

Google’s Willow, a 105-qubit transmon processor, scored 216 QUOPS at 2.0 × 10⁷ QUOPS per second. IBM’s ibm_boston, a 156-qubit machine with degree-3 connectivity, scored 204 QUOPS at 3.1 × 10⁵ QUOPS per second. Quantinuum’s H2-1 scored 1,320 QUOPS at 353 QUOPS per second, and its newer Helios-1 scored 1,504 QUOPS at 303 QUOPS per second. Discarding shots in which leakage errors were detected raised Helios-1 to 1,824 QUOPS at 247 QUOPS per second.

The same team encoded up to eight logical qubits in the ⟦7,1,3⟧ Steane code on Helios-1 and ran QUOPS circuits on that fault-tolerant architecture. Its scored result was 40 QUOPS at 4.9 QUOPS per second, at a circuit width of four. The authors state that the code was chosen for simplicity rather than for maximum QUOPS performance, and that the experiment does not saturate what Helios-1 can do fault-tolerantly.

The authors converted published resource estimates for two challenge problems into QUOPS targets. Factoring RSA-2048, using Craig Gidney’s 2025 estimate, requires approximately 2.5 × 10⁸ QUOPS at 5.7 × 10³ QUOPS per second. Estimating an energy eigenvalue of the FeMoco molecule, using resource estimates from Low and colleagues, requires approximately 3.4 × 10⁸ QUOPS at 8.0 × 10² QUOPS per second. Current processors have, or nearly have, the required throughput and fall short on capability by roughly five orders of magnitude, the authors reported.

Sandia’s work was funded in part by the Department of Energy Office of Science through the Quantum Systems Accelerator and by Sandia’s internal research programme. IBM hardware was accessed through Air Force Research Laboratory resources. NVIDIA published a QUOPS reference implementation in CUDA-Q on 14 September, the same day Quantinuum published a description of the benchmark.

My Analysis

Reconstructing eight years of published benchmark data, the authors find that quantum computational capability has doubled about every 1.4 years at Quantinuum and about every 2.1 years at IBM. Roadmaps promising scientifically transformative machines in the early 2030s need that rate to quadruple. Nobody has been able to state that requirement as a number before, because there was no measurement that ran across platforms and the physical-to-logical boundary.

The measurement itself is bleaker than the trend. Helios-1 scored 1,504 QUOPS on physical qubits and 40 on the error-corrected architecture built from the same ions, and the challenge problems the authors chose need 2.5 × 10⁸ and 3.4 × 10⁸. Where the machines already have the throughput those problems require, they fall five orders of magnitude short on the size of circuit they can finish.

Although neither number settles when a useful quantum computer arrives, both change what a roadmap has to show before anyone should believe it.

What QUOPS actually measures

For six years the field’s flagship system-level number was quantum volume, and it ran out of road for two reasons the QUOPS authors state plainly. Verifying a quantum volume result costs classical compute that grows exponentially with qubit count, so the benchmark stops being runnable exactly when the machines get interesting. And a quantum volume of 2ⁿ certifies square circuits of width and depth n, which is a shape that has little to do with the shape of a useful algorithm.

QUOPS replaces the square with a region. A machine’s capability region is the set of circuit shapes (w, s) it can execute with a mean process polarization of at least 1/√e, roughly 61%, established as the lower bound of a 95% confidence interval. Width plotted against size gives a boundary, the largest circuit a machine completes at each width, rather than a single point.

The single-number score comes from a constraint the authors call the admissible cone: w² ≤ s ≤ w³. Circuits below w² are shallow enough to simulate classically, and the upper bound reflects the observed shape of resource estimates for the problems people actually want to solve. Published estimates put utility-scale circuits at around 10³ qubits with effective sizes between 10⁶ and 10⁹, which is the range the cone is built to point at.

One thing the unit is not: a count of native hardware gates. QUOPS defines an architecture-independent circuit size and then compiles those circuits into each machine’s native or logical operations, so routing, synthesis and error-correction costs are all included in the score. Because of that design, a QUOPS number can be compared across platforms but not with a vendor’s gate count.

The verification problem is solved with mirror circuits, a technique Proctor and Blume-Kohout developed in 2021. A mirror circuit runs a random circuit forward, applies a Pauli layer, then runs the inverse, so the ideal output is a known bit string. That lets the team estimate polarization without classically simulating the forward circuit, which is what keeps the benchmark runnable as machines scale past practical classical simulation.

The cone’s upper bound binds. Willow’s maximizing shape was (6, 216), and 6³ is exactly 216, so its reported score equals the ceiling the definition draws at that width. The team mapped Willow’s full capability region and found width 6 to be its maximizing width, so wider circuits did not produce a higher score. It remains a definitional edge, and anyone comparing Willow to Helios-1 on this one number should know it is there. Willow also beat its own noise model, which put its maximizing shape at (6, 144).

What the four scores say about architecture

Trapped-ion machines win capability by a factor of six to seven: Helios-1’s 1,504 against Willow’s 216, H2-1’s 1,320 against ibm_boston‘s 204. Superconducting machines win throughput by up to five orders of magnitude. Practitioners already understood the qubit connectivity and physics that produce both results, and the benchmark’s contribution is converting a qualitative trade-off into two numbers you can put in a table.

Willow’s qubits occupy a degree-4 lattice and ibm_boston‘s a degree-3 heavy-hex lattice, per IBM’s own processor documentation, so a CNOT between distant qubits requires a chain of SWAPs. Quantinuum’s QCCD architecture physically moves ions, which gives all-to-all connectivity and substantially reduces that routing penalty. The capability regions make the connectivity penalty visible; the paper does not isolate routing as the sole cause of the score difference, and neither should anyone quoting it.

What the trapped-ion machines buy with that connectivity is width without collapse. Helios-1 executed size-1,504 circuits at width 16, size-1,408 at width 32, size-1,280 at width 64 and size-881 at width 98. Capability declines across that range rather than falling off a cliff, which is the opposite of what the transmon regions show.

The cost appears in the supplementary data rather than the headline numbers, and it is steep. The width-16 measurement that produced the 1,824-QUOPS postselected result took 397 minutes for 4,000 shots, and that run failed the raw threshold, passing only after leakage postselection. At width 98, postselection discarded 51.4% of shots in the May run and 40.5% in the July run. Helios-1’s headline rate is 303 QUOPS per second, against Willow’s 20 million.

Error mitigation changes the shape of the trade rather than resolving it, and the evidence for it is weaker than for the headline scores. Lowering the success threshold to 1% polarization, which implies a sampling overhead of up to 10⁴, lifts Willow to 651 QUOPS, ibm_boston to 899, H2-1 to 7,796 and Helios-1 to 20,442. The authors are explicit that these regions come from a combination of directly measured and extrapolated data, so they do not carry the evidentiary weight of the 1,504 figure. Where the increases of three to eleven times are real, they cost three to four orders of magnitude of throughput: Helios-1 at 20,442 QUOPS runs at 0.29 QUOPS per second.

The encoded Helios-1 scored 2.7% of the raw machine

The single most useful comparison in this paper comes from one machine in two configurations. Helios-1 running on physical qubits scored 1,504 QUOPS on 2 June. Helios-1 running logical qubits in the ⟦7,1,3⟧ Steane code scored 40 QUOPS, at width four, in runs on 28 June and 29 August. Same hardware, same laboratory, roughly 2.7% of the capability.

That is the cost of this code on this machine, not the cost of fault tolerance as such. The paper says so directly: the Steane code was chosen for simplicity rather than for optimal QUOPS performance, and the experiment does not saturate Helios-1’s fault-tolerant capability. Higher-rate codes, higher-fidelity magic states and direct fault-tolerant T gates are all already demonstrated elsewhere and would all move the number.

What the experiment does establish is real. The circuits are fault tolerant at distance three: no single fault propagates to an uncorrectable error. Cliffords run transversally, and T gates are implemented by magic state injection through a dynamically generated auxiliary Steane block. Logical zero preparation uses Goto’s circuit, while the logical T state uses flag qubits with repeat-until-success. That is a construction-level guarantee rather than a demonstration of scalable below-threshold computation.

The development history in the supplement is the part vendors do not usually publish at this level of operational detail. Version one scored 24 QUOPS on 9 June. Two days later an attempt at size 32 failed: the polarization estimate came in at 0.565 with a 95% lower bound of 0.455, well under the 0.607 the test requires of the lower bound. Version two, with higher-fidelity magic states and per-shot randomization, reached 40 QUOPS on 28 June, taking 239 minutes. Version three, on 29 August, kept the score at 40 and cut the runtime to 73 minutes by enforcing composable fault tolerance and applying error correction only where fault tolerance required it. That took the rate from 1.3 to 4.9 QUOPS per second. Three iterations, one public failure, a 3.8× rate improvement on fixed hardware, all of it from software and error-correction design.

At width 8 the eight-logical-qubit configuration executed circuits of size 16, and the cone requires size to equal or exceed w², which is 64 at that width. The widest logical demonstration therefore contributes nothing to the score. Eight logical qubits is a real achievement and a real headline; eight logical qubits doing computationally relevant work is a different claim, and QUOPS distinguishes them.

Size is the bottleneck, not speed

The comparison that surprised me most is between the two target numbers and the measured rates. RSA-2048 needs about 5.7 × 10³ QUOPS per second to finish within five days; FeMoco needs about 8.0 × 10² in the same window. Willow already runs at 2.0 × 10⁷ QUOPS per second, clearing both by three to four orders of magnitude. ibm_boston, at 3.1 × 10⁵, clears RSA-2048 by a factor of 54 and FeMoco by a factor of 388. The paper’s own hedge is that today’s processors have, or nearly have, the necessary rate. The comparison is conservative in the machines’ favour by at most a factor of e, because the reported rate attenuates the raw rate by measured polarization while the targets do not.

What none of them can do is execute a circuit anywhere near large enough. Today’s processors are five orders of magnitude short on circuit size, while Willow and ibm_boston already exceed the rate both problems require. Much of the public conversation assumes quantum machines are simply too slow, and for trapped ions that is true. A superconducting processor is limited by how many operations it can run before the answer becomes noise, and its clock speed is already sufficient for a useful chemistry calculation.

That distinction has a practical consequence for reading hardware roadmaps. IBM says its Nighthawk r2 delivers roughly a 25-fold increase in circuits executed per second over the Heron fleet. Take the vendor claim at face value and it is still an improvement on the axis that is not currently binding for these two challenge problems, and circuits per second is not the same metric as QUOPS per second, which folds in polarization and discarded shots. Throughput will bind later, once fault tolerance drags the effective rate down by the factors the projections show. For now an improvement in circuit size is worth more than an improvement in circuit rate, and QUOPS lets you say that with numbers instead of intuition.

What the challenge-problem targets are, and what they are not

Both targets are derived, not measured, and the authors are careful about it in a way the coverage is not. The procedure converts the number of Toffoli gates into a T count, estimates the logical T-gate error rate at which one execution would clear the polarization threshold, then works out what QUOPS score a machine capable of that error rate would post. For RSA-2048 the inputs are 1,399 logical data qubits and 7.1 × 10⁸ Toffoli gates from Gidney’s 2025 estimate. For FeMoco they are 1,459 qubits and 1.0 × 10⁹ Toffoli gates from Low and colleagues.

The conversion assumes four T gates per Toffoli, which holds for the compute-uncompute AND constructions that dominate both algorithms. Assume the seven T gates that exact Toffoli synthesis requires and the targets become 4.2 × 10⁸ and 5.9 × 10⁸. The method also ignores Clifford errors in both the algorithm and the benchmark circuits, ignores idling errors, and uses one particular rotation synthesis cost model. The authors put the total uncertainty at roughly a factor of two, which does not trouble a conclusion about five orders of magnitude but should trouble anyone quoting 2.5 × 10⁸ as though it were measured.

There is a second point about these targets that resolves something readers have been whipsawed by for two years. Physical-qubit estimates for RSA-2048 have fallen from 20 million in 2019 to under a million in Gidney’s 2025 revision to under 100,000 in the qLDPC-based Pinnacle proposal. The QUOPS target does not change with them. The target is keyed to logical work – how many non-Clifford operations the algorithm requires and how accurately each must execute – and improvements in error-correcting codes change how many physical qubits you must buy in order to deliver that logical work. The falling headline numbers describe the price of the machine. The QUOPS target describes the job.

That is a useful thing to be able to say cleanly, because the two number series have been reported side by side for two years as though they were in tension.

The trend line, and what it demands of the roadmaps

To get a history, the team reconstructed QUOPS scores for IBM and Quantinuum processors back to 2018 from published quantum volume data. For IBM they matched compiled two-qubit gate counts, arriving at a smooth approximation of 2.5[log₂(QV)]². For Quantinuum, where raw heavy-output data was available, they inferred an effective two-qubit gate fidelity and converted that. Both conversions assume a global depolarizing error model.

Extended unchanged, doubling every 1.4 years for Quantinuum and every 2.1 for IBM, the resulting curves reach the capability the challenge problems require somewhere between 2050 and 2070.

That number is going to be quoted badly, so I want to put the authors’ own framing next to it. They do not present 2050–2070 as a forecast. They present it as the thing that happens if the physical-qubit path continues unchanged, and then they show why it cannot. Under the paper’s error model, physical-qubit capability approaches a ceiling of roughly 1/(2ε), where ε is the physical error rate, with connectivity constraints lowering it further. The authors put that ceiling at about 330 QUOPS for a degree-4 lattice and about 10⁴ QUOPS for a fully connected machine, no matter how many qubits are installed. Their words for exceeding 10⁴ QUOPS on physical qubits are that it would be remarkable and surprising. The 2050–2070 line is an argument for fault tolerance, not a prediction of when anything arrives.

The only directly measured historical points are the 2026 ones. Everything before that is inferred through a depolarizing model from quantum volume announcements, and the inference appears to run optimistic at the top of the range: the method gives 302 QUOPS for IBM’s Pittsburgh processor from its August 2025 quantum volume of 2¹¹, while direct measurement of ibm_boston produced 204. Those are different machines of the same generation, and the paper already warns that quantum-volume-derived points are good to about a factor of two. A 32% shortfall is inside that stated tolerance rather than a calibrated error on the doubling time. A reader should still know that the reconstructed score is the higher of the two, because the doubling rate is the input to the 2050–2070 figure, which is the number people will repeat.

Roadmaps projecting scientifically transformative capability in the early 2030s need this trend to quadruple. The test is falsifiable and the benchmark for applying it ships inside NVIDIA’s CUDA-Q, so every vendor claiming early-2030s utility now has a number to beat and a public method for beating it.

Putting the DOE’s own targets on the same axis

The citation behind that early-2030s sentence is not a vendor roadmap. It is the Blueprint for DOE Quantum Supercomputing, co-authored by Blume-Kohout, who is also senior author of this paper. The Blueprint sets out to deploy initial scientifically relevant quantum computing capability by 2028 and to mature what the DOE calls scientific utility through the early-to-mid 2030s. A Sandia team has published a benchmark that quantifies what its own department’s blueprint requires, which I read as a sign of institutional health rather than the opposite.

The DOE has since put money behind those dates. Quantum Genesis, announced in June 2026, aims to demonstrate fault-tolerant systems with logical qubit counts in the low hundreds by 2028, through a milestone-driven competition run with the national laboratories.

So what does the paper’s own analysis say such a machine would score? Its projections cover two families. A degree-4 surface code architecture with cultivation, at a uniform 0.1% gate error rate, is projected in the supplement at 1,950 QUOPS on 5,000 physical qubits, 9,240 on 10,000, 68,470 on 25,000 and 273,632 on 50,000. A fully connected architecture with 10⁻⁵ single-qubit and 10⁻⁴ two-qubit error rates reaches 6.7 × 10⁴ QUOPS on 1,000 physical qubits, 3.7 × 10⁵ on 5,000 and 2.2 × 10⁶ on 10,000.

Two observations follow, and the second is my arithmetic rather than the paper’s.

First, look at the bottom of the first family. A 5,000-physical-qubit surface-code machine is projected at 1,950 QUOPS, against the 1,504 that 98 trapped ions deliver today with no encoding at all. The overhead visible in the Helios-1 experiment persists in the projections.

Second, the paper’s best projected fault-tolerant machine reaches 2.2 × 10⁶ QUOPS. RSA-2048 needs 2.5 × 10⁸ and FeMoco needs 3.4 × 10⁸. Every architecture the authors model, including the aggressive fully connected one, falls roughly two orders of magnitude short of both.

I am not going to convert the DOE’s 2028 target into a QUOPS number. The widths in the paper’s projection table are benchmark circuit widths, not counts of the logical qubits a device hosts. A 50,000-qubit surface-code machine hosts considerably more logical qubits than the 68 at which its best score is attained, because ancilla patches and routing space consume the difference. Setting that 68 next to the DOE’s low hundreds compares two different quantities.

What can be said is narrower and still useful. The paper models no machine at the DOE’s target scale, and every machine it does model scores roughly two orders of magnitude below what the challenge problems require. Closing the remainder requires lower error rates, more qubits, or better logical architectures than anything the authors analysed.

I do not read these projections as a case against Quantum Genesis. Low hundreds of logical qubits in 2028 would be an extraordinary engineering result and would change what is possible in quantum chemistry and materials well before anyone gets near FeMoco’s full resource estimate. A 2028 fault-tolerant machine and one that solves a canonical challenge problem are still separated by orders of magnitude, and QUOPS gives a programme manager a common scale on which to see the distance.

The milestone I would actually watch

The authors name a specific, near-term, falsifiable event: the first time a fault-tolerant architecture posts a QUOPS score higher than every physical-qubit architecture. That is Gottesman’s criterion for demonstrating fault tolerance, restated as a measurement others can reproduce under a published specification.

Their estimate of the requirement is 20 to 30 logical qubits encoded in 1,000 to 5,000 physical qubits, using encodings that are already well understood, which they project would comfortably exceed 10⁴ QUOPS against the roughly 10⁴ physical-qubit ceiling. They also note recent advances in error correction and logical architecture that could lower those costs substantially, and say the milestone could be achieved rapidly.

Helios-1 ran eight logical qubits at distance three, scoring on four. The error-correction work of the last eighteen months has produced higher-rate codes, better magic state cultivation, and direct fault-tolerant implementations of gates that currently require synthesis. A jump from 40 QUOPS to 20–30 logical qubits above 10⁴ QUOPS is large, and it is the kind of jump that below-threshold operation and improved decoders were supposed to make possible.

If a fault-tolerant architecture outscores every physical-qubit one in 2027 or 2028, the 2050–2070 extrapolation becomes irrelevant, which is what the authors intend it to become. If that has not happened by 2030, the fourfold acceleration the early-2030s roadmaps require will be very hard to argue for. Either way there is now a common measurement to settle it on, rather than a contest between roadmaps.

What I would not conclude from this paper

It is not an independent scorecard, and nobody involved claims it is. Quantinuum co-authored the benchmark and Quantinuum machines post the top capability scores on it. That is a real conflict and it belongs in every summary. It is also weaker than it looks: Sandia’s Quantum Performance Laboratory led the work and has spent a decade building the characterization methods underneath it, Google researchers Ryan Byrne and Eliott Rosenberg ran the Willow experiments and helped analyse the data, and the method is published in full with a reference implementation. That implementation ships through a vendor toolchain, a caveat whenever the benchmark is described as vendor-neutral. The asymmetry that concerns me more is IBM‘s. IBM did not participate; access came through Air Force Research Laboratory resources. And ibm_boston is a Heron-generation device. Because Nighthawk, the 120-qubit square-lattice architecture whose second revision shipped this month, was not on the bench, the 204 QUOPS result should not be read as a score for IBM’s current portfolio.

It is not a Q-Day prediction, in either direction. The RSA-2048 target is one of two challenge problems in the paper and the further of the two; FeMoco is the nearer one and the one the authors’ own funder is chasing. Reading 2050–2070 as an arrival date inverts the argument the authors are making, and quoting five orders of magnitude as proof that quantum computing is stalled ignores the fault-tolerant projections that occupy the second half of the paper. The authors wrote that the path to utility-scale capability will be expensive, creating strong incentives for hype and placing a premium on objective analysis, and both misreadings are forms of that hype.

It is not the last benchmark. The authors say so themselves, and the design is modular: QUOPS circuits are direct proxies for rotation-heavy Hamiltonian simulation and only indirect proxies for the Toffoli-heavy structure of factoring and chemistry algorithms, and the paper explicitly allows other circuit families to replace them. Quantum volume took six years to become a standard and then became a marketing number. QUOPS will face the same pressure.

What it is, on balance, is the first time anyone has put physical- and logical-qubit computation on the same scale and published the result with the failures included. For a field where “we have logical qubits now” has become a press release genre, a measurement showing that one encoded machine delivered 2.7% of its own raw capability is the most clarifying thing published this year. The utility ladder now has rungs you can measure.