QUOPS: A Quantum Benchmark That Reads 1,504 on the Best Machine — Breaking RSA-2048 Needs 250 Million

> 1,504 and 250 million are in the same unit.

The former is the score of today's best quantum computer on a new yardstick called QUOPS; the latter is the score needed to factor RSA-2048. Between them lie five orders of magnitude. QUOPS was led by Sandia National Laboratories with participation from Quantinuum and NVIDIA, posted to arXiv on September 10, detailed 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 a single methodology, with the conclusion compressed into one trackable number.

Why Previous Benchmarks Fell Short

The quantum hardware field has long been criticized for "spec-sheet theater": qubit counts say little if noise is too high to sustain large circuits. Raw qubit counts, two-qubit gate fidelities, and gate speeds remain useful for engineering diagnostics but fail to predict system-level performance — and break down entirely once fault-tolerant error correction is introduced.

IBM's Quantum Volume (QV, 2019) was the first single-number system benchmark, with three documented gaps:

• Classical verification cost grows exponentially with qubit count
• Loose correlation with real computational utility
• Only measures square circuits (width = depth), which real workloads almost never are

QUOPS addresses all three: it runs random circuit layers varying both width and size (single-qubit rotations plus 2× the CNOT count), covering shapes from wide-shallow to narrow-deep. It uses mirror circuits to estimate average process polarization without classical simulation of each target circuit. It captures the combined effect of compilation, error correction, syndrome decoding, and error mitigation, with explicit anti-gaming clauses preventing vendors from optimizing one dimension while hiding weaknesses elsewhere.

Two Numbers: Q and Ω

• Q: the largest benchmark circuit scale a system executes successfully, judged by estimated average process polarization reaching \(1/\sqrt{e} \approx 61\%\) at 95% confidence — meaning the output still carries signal, not just noise. Scores are only awarded in a restricted region where circuit size falls between width² and width³, corresponding to proposed practical workloads.
• Ω: effective quantum operations per second at the winning circuit shape, adjusted for error-mitigation sampling cost and post-selection discards.

Both matter: a machine that sustains large circuits but takes a week, and one that finishes instantly but collapses at depth 30, solve 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 tells the story. Helios-1 leads on sustainable circuit scale by ~7×; Willow runs ~66,000× more operations per second but sustains only one-seventh the circuit size. The physics: ion traps are nearly fully connected but slow to switch; superconducting qubits switch in nanoseconds but only talk to neighbors, so long-range circuit pairs must be routed across a grid, consuming error-correction budget. Procurement should therefore match architecture to workload, not rank on a single score.

Logical Qubits on the Same Yardstick

The team ran a full fault-tolerant architecture on Helios-1, encoding up to 8 logical qubits with the Steane [[7,1,3]] code, performing fault-tolerant state preparation, correction, Clifford operations, and magic state injection. The logical score was 40 (width 4) at 4.9 QUOPS/sec (up from 24 and 1.3/s in an earlier version, thanks to better magic states, per-shot randomized compiling, selective correction, and improved parallelism). The lower score vs. 1,504 physical quantifies error-correction overhead; the paper notes the chosen Steane scheme favored simplicity and did not exhaust Helios-1's fault-tolerance.

How Far from Commercially Useful?

Mapping published resource estimates onto QUOPS:

• RSA-2048 factoring: ~250 million (finishing in 5 days would need ~5.7×10³ ops/sec)
• FeMoco ground-state energy: ~340 million (~8.0×10² ops/sec)

The conversion from logical Toffoli counts is explicitly approximate and architecture-dependent. The gap is five orders of magnitude — the hardest quantifiable statement yet of quantum utility. Notably, on throughput, Willow already exceeds the required rate by ~3,500×; what fails is the scale of a single computation (roughly a million times too small).

The Sharpest Finding: More Qubits Won't Help

Extrapolating to degree-4 connectivity (the superconducting grid layout), the authors find such systems cap at ~330 QUOPS, regardless of qubit count. Willow's best circuit used 66 qubits for 216. Adding a thousand more qubits widens the chip but doesn't lengthen any single computation, because error accumulates with weighted gate count — extra qubits don't make individual gates cleaner. To push circuit scale: change connectivity (new architecture or modular interconnects) or reduce per-gate error rates. If the goal is circuit scale rather than throughput, the marginal return of stacking qubits is near zero.

Error Mitigation Accounting

Relaxing the polarization threshold from 61% to 1% raises scores 3–11× but drops effective rates by 3–4 orders of magnitude, since sampling overhead can reach 10,000×. Several error-mitigated boundary points rely on interpolation/extrapolation, so standard (unmitigated) scores serve as the cleaner direct-comparison baseline.

Caveats

• The paper is a September 10 preprint, not yet peer-reviewed
• First data covers only 4 machines
• Sandia led, but Quantinuum participated in designing the benchmark — and its hardware tops the Q dimension; independent third-party reproduction is a prerequisite for industry-standard status
• Timing note: DARPA's Quantum Benchmarking Initiative (QBI) Stage A proposals close September 30; QUOPS arrives just before. Quantinuum's blog calls on vendors to report both Q and Ω and on buyers to write QUOPS thresholds into RFPs
• The benchmark's effect: it replaces the "which modality wins" debate with an engineering-and-procurement debate — trapped ions lead circuit scale ~7×, superconducting leads throughput 3–4 orders of magnitude

References

1. Sandia National Laboratories, Quantinuum, NVIDIA et al., "QUOPS" preprint, arXiv (presented at IEEE Quantum Week) 2. Tech Times, "QUOPS: New Quantum Benchmark Compares Google, IBM, Quantinuum for First Time" — 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" — https://quantum-brief.com/blog/news-2026-09-16-quops-benchmark-utility-gap 4. FreeQuantumComputing, "QUOPS Measures Quantum Computing's Five-Order Utility Gap" — https://www.freequantumcomputing.com/blog/quops-quantum-computing-benchmark 5. Quantinuum official blog on QUOPS