QUOPS: A Public Ruler for Quantum Computing

1504 and 250 million are measured in the same unit.

The former is the score of today's best quantum computer on a new benchmark; the latter is the score needed to factor RSA-2048. Between them lies five orders of magnitude. The ruler is called QUOPS, led by Sandia National Laboratories with participation from Quantinuum and NVIDIA, posted to arXiv on September 10, explained by Quantinuum on September 14, and formally presented at IEEE Quantum Week. It is the first time Google, IBM, and Quantinuum processors have been compared under one methodology, with the result compressed into a single number that can be tracked year over year.

Why Previous Rulers Fell Short

The quantum hardware field has long been criticized for "spec-sheet theater." A machine can claim thousands of qubits, but if those qubits are too noisy to sustain large circuits, the number says little about real computation. Conversely, systems with fewer but higher-quality, well-error-corrected qubits may perform far better on real workloads.

Raw qubit counts, two-qubit gate fidelities, and gate speeds remain useful for engineering diagnostics, but they cannot predict system-level performance and break down entirely once fault-tolerant error correction enters the picture.

IBM's Quantum Volume (QV), introduced in 2019, was the first attempt at a single holistic score and became the field's flagship system-level benchmark. It has three documented gaps:

1. Classical verification cost grows exponentially with qubit count 2. Only loose correlation with real computational utility 3. Measures only square circuits (width equals depth), while real workloads almost never are

QUOPS targets all three. It runs random circuit layers varying in both width (qubit count) and size (count of single-qubit rotations plus twice the number of two-qubit CNOTs, since two-qubit gates cost roughly double), covering shapes from wide-and-shallow to narrow-and-deep. Measurement uses mirror circuits to estimate average process polarization without classical simulation of each target circuit.

Crucially, it captures the combined effect of compilation, error correction, syndrome decoding, and error mitigation—not isolated components. The framework includes explicit anti-gaming clauses, so vendors cannot optimize one dimension while hiding weaknesses elsewhere.

Two Numbers: Q and Omega

The ruler outputs two interlocking numbers:

• Q: the largest benchmark circuit size a system can successfully execute, defined as achieving an estimated average process polarization of \(1/\sqrt{e} \approx 61\%\) at 95% confidence. This threshold means the output still carries signal rather than pure noise. Scoring only counts a restricted region: circuit size must fall between width squared and width cubed, corresponding to the shape of proposed practical workloads. Narrow, shallow circuits score nothing no matter how well they run.
• Omega: the effective quantum operations per second for the circuit shape that produced the Q score, adjusted for error-mitigation sampling cost and post-selection discards.

Both numbers matter. A machine that can sustain large computations but takes a week, and one that finishes instantly but collapses at depth 30, face entirely different problems.

Four Machines, No Single Winner

| Processor | Physical Qubits | Q Score | QUOPS/sec | Best Circuit Width | |---|---|---|---|---| | Quantinuum Helios-1 | 98 | 1504 | 303 | 16 | | Quantinuum H2-1 | 56 | 1320 | 353 | 12 | | Google Willow | 105 | 216 | 2.0×10⁷ | 66 | | IBM ibm_boston | 156 | 204 | 3.1×10⁵ | — |

No single column can be read alone. Helios-1 leads in sustainable circuit scale by roughly 7x; Willow runs about 66,000x more operations per second but sustains only one-seventh the circuit size.

The physics is straightforward: trapped ions are nearly fully connected but slow to switch; superconducting qubits switch on nanosecond timescales but talk only to neighbors, so circuits requiring distant qubit pairs must route information across the grid, consuming error-correction budget along the way.

For buyers, the conclusion is scenario-based selection, not a single-number ranking. Workloads needing large circuits at low speed, and workloads needing high throughput with limited circuit size, are simply different categories.

Logical Qubits on the Same Machine

The team also ran a complete fault-tolerant architecture on Helios-1, encoding up to 8 logical qubits with the Steane [[7,1,3]] code, performing fault-tolerant state preparation, error correction, Clifford operations, and magic state injection.

The logical-implementation score is 40 (width 4) at 4.9 QUOPS/s, up from 24 in an earlier version. The score roughly doubled thanks to better magic states and pauli twirling; the rate rose from 1.3 to 4.9 via selective error correction and improved parallel execution.

40 is far below Helios-1's 1504 on physical qubits. The goal was not to win numerically but to verify the same ruler can measure both physical and logical layers, and that changes in compilation and error-correction design are visible to it. The paper notes the chosen Steane scheme favored simplicity and did not fully exploit Helios-1's fault-tolerance capabilities.

How Far From Commercially Useful Computation

The paper maps two published resource estimates onto the QUOPS scale:

• Factoring RSA-2048: ~250 million QUOPS
• Estimating the ground-state energy of FeMoco (nitrogenase's iron-molybdenum cofactor): ~340 million

The conversion starts from existing logical Toffoli counts and widths, then approximates equivalent non-Clifford work—an explicitly approximate, architecture-dependent step.

The gap is about five orders of magnitude—the hardest quantitative statement yet of quantum utility, turning "when will it be useful" from qualitative narrative into a trackable number.

Splitting rate and scale makes the picture more interesting: to finish RSA-2048 in 5 days would require ~5.7×10³ operations/s, and FeMoco ~8.0×10²/s. Willow's throughput already exceeds these thresholds by roughly 3,500x—but its sustainable circuit scale is about a million times too small. On the throughput side, superconducting hardware has already crossed the practical threshold; what's stuck is how long a single computation can run.

The Sharpest Finding: Adding Qubits Won't Fix It

The paper's most consequential conclusion comes from an extrapolation. Applying the analysis to degree-4 connectivity—superconducting-chip grid layouts—the authors find such systems cap out near 330 QUOPS, regardless of qubit count.

Willow's best circuit used 66 qubits for a score of 216. Adding a thousand more qubits makes the chip wider, not any single computation longer, because errors accumulate with weighted gate count and extra qubits don't make individual gates cleaner.

The roadmap implication is direct: if the goal is circuit scale rather than throughput, the marginal return on stacking qubits approaches zero. To go higher, architectures must change connectivity (or adopt modular interconnects) or drive down individual gate error rates.

The Error Mitigation Accounting

The paper also quantifies error mitigation's cost. Relaxing the polarization threshold from 61% to 1% boosts each tested system's score by 3–11x, but effective rates drop by three to four orders of magnitude, since sampling overhead can reach 10,000x. Because several error-mitigated boundary points relied on interpolation or extrapolation, the paper treats standard (unmitigated) scores as the cleaner direct-comparison baseline.

Necessary Caveats

• The paper is a September 10 preprint, not yet peer-reviewed
• First data covers only 4 machines
• The benchmark is Sandia-led, but Quantinuum participated in its design, and its hardware scores highest on Q
• Independent third-party replication and broader platform testing are prerequisites for industry-standard status

One timing detail stands out: the new DARPA Quantum Benchmarking Initiative (QBI) Stage A proposal deadline is September 30, and QUOPS pushed a unified score into government procurement view just before it. Quantinuum's blog calls on vendors to report both Q and Omega together, and on buyers to write QUOPS thresholds into RFPs. Whether that lands depends on how many non-interested parties submit scores.

The displacement of Quantum Volume also carries a side effect: it transforms the "technology-race debate" into an "engineering and procurement debate." Trapped ions lead circuit scale by ~7x; superconductors lead throughput by three to four orders of magnitude. The two routes' capability envelopes have different shapes—they can no longer be ranked in one sentence.

Sources

1. Sandia National Laboratories, Quantinuum, NVIDIA et al., "QUOPS" preprint, arXiv, 2026-09-10 (presented at IEEE Quantum Week 2026) 2. Tech Times, "QUOPS: New Quantum Benchmark Compares Google, IBM, Quantinuum for First Time", 2026-09-15 — https://www.techtimes.com/articles/327543/20260915/quops-new-quantum-benchmark-compares-google-ibm-quantinuum-first-time-all-trail-100000x.htm 3. Quantum Brief, "Quantum's new yardstick reads 1,504. Breaking RSA needs 250 million", 2026-09-16 — https://quantum-brief.com/blog/news-2026-09-16-quops-benchmark-utility-gap 4. FreeQuantumComputing, "QUOPS Measures Quantum Computing's Five-Order Utility Gap", 2026-09 — https://www.freequantumcomputing.com/blog/quops-quantum-computing-benchmark 5. Quantinuum official blog (QUOPS explanation and vendor reporting appeal), 2026-09-14