Quantum Volume vs. Algorithmic Qubits: what do vendor metrics actually measure?

Status as of: August 5, 2026.

Every quantum hardware vendor publishes a headline number. The numbers are real, the measurements are (as far as anyone can verify) honestly run — and they still cannot be compared, because each metric was designed by the vendor whose machine it flatters. This post is a map of the rulers, not of the machines.

What are the four numbers on the table?

Four numbers, four owners, four different questions. None of them answers "which machine solves my problem" — that question needs an instance-level benchmark against a classical baseline (how a weak baseline ruins one).

Why did each vendor pick its own ruler?

Because each ruler rewards a different physics. This is the structural point: a metric is a choice of what to count, and every vendor counts where its architecture is strong.

Quantum Volume rewards fidelity and connectivity, not size. A QV test runs square random circuits — n qubits, n layers — so a machine with few, slow, high-fidelity, all-to-all-connected qubits (a trapped-ion machine) scores exponentially better than a machine with many fast qubits on a 2D grid that must burn SWAP gates to connect distant pairs. Quantinuum adopted QV as its headline metric in 2020 with a public pledge to grow it 10× per year (The Quantum Insider, May 13, 2025) and delivered: 2^23 on H2 in May 2025, 2^25 = 33,554,432 on the 56-qubit H2-1 by September 2025.

IBM — the metric's author — stopped leading with it. In November 2023 IBM introduced layer fidelity and error-per-layered-gate (EPLG, arXiv:2311.05933) and wrote that on large devices QV "only samples a tiny part of the system," spotlights "a handful of the device's best qubits," was "designed to run on all-to-all connected systems," and will "soon become too large for us to simulate classically" (IBM Quantum blog, Nov 20, 2023). All four statements are technically defensible. It is also true that the replacement metric — chains of layered gates — fits IBM's 2D heavy-hex and square lattices, where QV did not. Both things can be true at once; that is what a framing choice looks like.

Algorithmic Qubits rewards the software stack on top of the hardware. IonQ's #AQ counts the largest N where QED-C-derived algorithm circuits (N qubits, up to N² entangling gates) pass a 37% fidelity threshold — with compilation and error mitigation allowed inside the number. IonQ presents this as a feature: it measures "structured quantum circuits of practical relevance," not random ones (IonQ resource page). Its September 25, 2025 press release put #AQ 64 on the Tempo system, and IonQ's October 13, 2025 blog attributes the jump from #AQ 36 partly to "dramatically improved error mitigation and compiler capabilities" — the vendor says openly that part of the score lives in software.

Qubit count and CLOPS reward fabrication scale and gate speed. Superconducting qubits are lithographed and switch in nanoseconds; trapped ions are loaded and shuttled physically. So IBM holds both crowns: 1,121 fabricated qubits (Condor, Dec 2023) and 330,000 CLOPS with two-qubit fidelity above 99.9% on more than 50% of tested pairs (Nighthawk, Nov 12, 2025). Quantinuum's Helios, launched the same month, leads the opposite column: ≈99.92% median two-qubit fidelity with all-to-all connectivity across 98 qubits (PostQuantum analysis, Nov 2025). Neither vendor headlines the other's column.

What happened when the metrics collided?

Three episodes show that the dispute is about definitions, not data.

Episode 1 — the author leaves its own metric (Nov 2023). IBM defined QV in 2019, then moved its public benchmarking to layer fidelity/EPLG when its devices passed 100+ qubits on 2D lattices. The stated reasons (sampling only the best qubits; classical simulation limits; all-to-all assumption) are documented above. The practical effect: from 2024 on, the QV leaderboard contains essentially one committed vendor.

Episode 2 — one vendor audits another's metric (Mar 1, 2024). Quantinuum published "Debunking algorithmic qubits," arguing #AQ can be inflated by choices inside the number: standard compilation (pytket) reduces the benchmark's phase-estimation circuits from 992 to 141 entangling gates (−85%) and amplitude estimation from 868 to 72; plurality-voting error mitigation closes performance gaps between machines of different quality; and in their simulation, a lower-fidelity machine with these techniques outscores a higher-fidelity one without them. Quantinuum's comparison at the time: H2-1 two-qubit fidelity 99.816% vs. 99.35% reported for IonQ Forte. Note what this exchange is and is not: Quantinuum did not claim IonQ's measurements were false — it claimed the metric's rules permit score improvements that don't come from hardware. IonQ, for its part, discloses that compilation and mitigation are part of #AQ and argues that is what users actually experience. Both positions are internally consistent. They are also mutually incomparable — which is the point of this post.

Episode 3 — dual records in the same month (Sep 2025), each under the reporter's own ruler. Quantinuum announced QV 2^25; IonQ announced #AQ 64. IonQ's October 2025 blog framed #AQ 64 as a computational space of 2^64 states, "36 quadrillion times larger" than IBM's publicly available systems — an arithmetic comparison across architectures made under IonQ's own metric. Each release is accurate under its own definition; neither can be checked against the other's.

How do you read a vendor metric announcement?

Five questions, in order. They are the same discipline as reading an advantage claim, applied to hardware numbers:

1. Who defined the metric? If the answer is "the vendor reporting it," treat the number as a self-graded exam. Honest, possibly — comparable, no.
2. What does the metric structurally reward? Connectivity and fidelity (QV), the compiler/mitigation stack (#AQ), fabrication count (qubits), gate speed (CLOPS). Check whether the machine's architecture is strong exactly there. It always is.
3. Is software inside the number? Compilation and error mitigation can move a score without touching the hardware (Quantinuum's 992→141 gate demonstration, Mar 2024; IonQ's own attribution of #AQ gains to compiler improvements, Oct 2025). Neither disclosure is hidden — but the number alone doesn't tell you.
4. Can a third party reproduce it under the same rules? QV and #AQ both have public protocols — reproduction happens rarely, and cross-vendor reproduction essentially never.
5. Is there a conversion between rulers? No published, peer-reviewed conversion exists between QV, #AQ, EPLG and CLOPS as of August 2026. Any sentence of the form "X's metric implies it beats Y" is crossing rulers without an exchange rate.

The failure mode these questions catch is the same one that produces fake crossover points and dequantized advantage claims: a comparison where one side chose the measuring stick.

What we don't know

• Whether any of these metrics predicts application performance. No published study demonstrates that a higher QV, #AQ, or CLOPS translates into better end-to-end results on a named industrial problem against a strong classical baseline. That mapping is exactly what the field lacks.
• How the machines would rank under a neutral ruler. The QED-C benchmark suite exists and is public, but scores are overwhelmingly self-reported by vendors on their own hardware; there is no independent body that runs all machines under identical rules on the same day.
• What the records are worth across time. Vendor metrics get retired when they stop flattering (QV's author left it in 2023; the remaining leaderboard has one committed participant). A record on a retired ruler is a fact about history, not about the current market.
• Rosetta has no proprietary measurements in this class. Our sealed runs (the V-0012 series) benchmark algorithms on problem instances, not hardware metrics; we have not run QV, #AQ, or EPLG protocols ourselves, and nothing here is a Rosetta measurement of any vendor's machine. This post is a reading of public, linked vendor claims — under our operating rule that a number is only comparable when both sides ran the same instance under the same rules with the referee outside the building.

Sources

• Cross et al., Validating quantum computers using randomized model circuits, PRA 100, 032328 (2019) / arXiv:1811.12926
• IBM Quantum blog — layer fidelity / EPLG (Nov 20, 2023)
• McKay et al., Benchmarking Quantum Processor Performance at Scale, arXiv:2311.05933
• IonQ — Algorithmic Qubits: A Better Single-Number Metric
• Quantinuum — Debunking algorithmic qubits (Mar 1, 2024)
• The Quantum Insider — Quantinuum QV 2^23, five-year pledge (May 13, 2025)
• Quantum Zeitgeist — Quantinuum QV 2^25 = 33,554,432 on H2-1 (Sep 2025)
• IonQ press release — #AQ 64 (Sep 25, 2025)
• IonQ blog — #AQ 64 on Tempo, error mitigation and compiler gains (Oct 13, 2025)
• Tom's Hardware — IBM Nighthawk: 120 qubits, 330,000 CLOPS, >99.9% 2Q on >50% of pairs (Nov 12, 2025)
• PostQuantum — Quantinuum Helios: 98 qubits, ≈99.92% 2Q fidelity, all-to-all (Nov 2025)
• IBM Newsroom — Condor, 1,121 superconducting qubits (Dec 4, 2023)

Rosetta Q publishes verdicts with reproducible raw data. This is educational content, not a product claim. No vendor named here paid for or reviewed this analysis; every vendor figure is linked to the vendor's own disclosure or to dated press coverage.