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There is no single score that fairly compares a quantum computer with a classical supercomputer. Compare them on the same defined task, at the same required result quality, and across the same end-to-end runtime boundary. Quantum volume, CLOPS and classical FLOP/s scores describe different things; none is a universal cross-platform speed measure.
What makes a fair comparison?
A quantum processor runs quantum circuits for selected tasks. A classical supercomputer runs conventional numerical and data-intensive workloads. Their headline hardware numbers are not interchangeable: qubit count does not translate into FLOP/s, and a quantum benchmark score does not say how long a classical system would take to solve the same useful problem.
Start with a named workload and define the quality of result that counts as success. Then make the system boundary explicit. Quantum execution usually sits inside a larger classical-quantum workflow: classical software compiles and schedules circuits, controls the device, and may process or mitigate errors in the results. A runtime comparison that omits material stages on one side but includes them on the other can mislead.
| Comparison axis | Quantum computer | Classical supercomputer | What to report |
|---|---|---|---|
| Work performed | The named quantum application or circuit | A classical implementation of the same task | Confirm both solve the same problem and produce equivalent outputs. |
| Result quality | Fidelity, error rate or target success probability | Accuracy or error tolerance | Require the same acceptable result quality. |
| Capacity | Circuit width and depth, or a stated capability region | Problem size, memory and workload limits | Describe the actual tested problem, not just peak hardware specifications. |
| Throughput | A named metric such as CLOPS, with its protocol version, or application-level throughput | A named benchmark such as HPL or HPCG | Keep benchmark names and units attached; do not equate unlike scores. |
| Time | End-to-end wall-clock time for the required result | End-to-end wall-clock time for the same result | State which setup, data movement, processing and error-handling stages are included. |
| Resources | Cost and energy, if measured | Cost and energy, if measured | Compare only figures measured on a like-for-like boundary. |
For a credible result, also record the device, software and runtime configuration, benchmark version, and measurement date. These details matter because benchmark protocols and reported system results can change over time.
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What quantum performance metrics do—and do not—tell you
Quantum volume: a square-circuit reliability test
Quantum volume compresses circuit width and depth into one figure. Its protocol tests square random circuits and validates performance through a Heavy Output Generation sampling task. The benchmark reference defines a score of 2n when a device validates circuits of size n.
The measure reflects several factors, including gate fidelity, coherence time, chip topology and transpilation. But the square-circuit profile is only one kind of workload, and the score focuses on a subset of a processor’s best qubits rather than necessarily representing the full chip. It is not an application runtime or a score that can be compared directly with a classical supercomputer’s FLOP/s.
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CLOPS: hybrid circuit throughput with protocol details
CLOPS measures how quickly a quantum system and its classical runtime execute batches of parameterized circuits. In the process IBM describes, circuits run sequentially, with the output of one informing the parameters of the next. The measure therefore includes classical processing as well as quantum execution. IBM Quantum’s 2023 post, “Updating how we measure quantum quality and speed,” describes CLOPS as “a measure of how quickly our processors can run Quantum Volume circuits in series, acting as a measure of holistic system speed incorporating quantum and classical computing.”
There are historical Quantum Volume-derived and hardware-aware forms of CLOPS. They define circuit layers differently; the hardware-aware version accounts for device connectivity and parallelizable gates. Before comparing two CLOPS values, check that they use the same protocol, layer definition and circuit conditions, and determine what their reported wall-clock time includes. A bare CLOPS figure is not enough to establish a task-level speed advantage.
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Application benchmarks and QUOPS
Application-oriented quantum benchmarks vary problem size and map output fidelity over circuit width and depth. Work associated with QED-C also describes measuring parts of the execution pipeline and time to solution. This kind of benchmark is closer to an application claim than a qubit count, but it establishes a quantum-versus-classical advantage only when a comparable classical implementation, matched quality target and transparent runtime boundary are provided.
Sandia’s QUOPS framework describes a quantum computer’s capability region: the programs it can execute successfully, organized by circuit width and gate count. It also defines a QUOPS rate for how quickly the system executes those units, with the stated intent of covering both physical-qubit and fault-tolerant systems. QUOPS is a quantum-side framework, not a conversion to classical FLOP/s or a replacement for a task-matched classical baseline.
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Which classical benchmarks should you use?
Classical supercomputer scores also depend on the workload and precision being measured. TOP500’s 65th-list report gives El Capitan a High-Performance Linpack (HPL) result of 1.742 exaflop/s. The same system entry reports 17.41 petaflop/s on HPCG, a complementary benchmark, and 16.7 exaflop/s on HPL-MxP, a mixed-precision benchmark. These are results in different benchmark categories, not three interchangeable measures of one general-purpose speed.
Those values belong to that specific TOP500 report; they are not timeless specifications or a claim about the current top-ranked system. For a current ranking, check the relevant list edition and the system’s submission details. In any comparison, name the benchmark and precision regime beside the number.
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How to compare performance step by step
- Specify the task. Name the problem and say whether it is a useful application or a special-purpose sampling or benchmark task.
- Set the success criterion. State the required accuracy, fidelity, error tolerance or success probability, and require both systems to meet it.
- Match the boundary. Decide whether time includes compilation, scheduling, setup, data movement, quantum execution, error mitigation or correction, and post-processing. Include material stages for both systems or clearly identify exclusions.
- Measure end-to-end time to solution. Report the wall-clock time needed to produce a result that meets the stated criterion. Keep benchmark-specific throughput scores separate rather than treating them as substitutes for task time.
- Report resources where evidence supports it. Compare energy and cost only when they have been measured for both systems using comparable boundaries; do not infer them from a throughput score.
- Make the result reproducible in context. Give the device, software and runtime configuration, benchmark version, and measurement date.
When does the evidence show a quantum advantage?
A quantum advantage claim needs evidence for a specific task and a fair classical baseline. The quantum result must meet the required output quality, and its stated runtime boundary must account for the relevant quantum-classical workflow. A quantum volume or CLOPS result alone does not demonstrate that a quantum computer is faster than a supercomputer on a useful application.
The cited sources do not establish a matched, end-to-end comparison of a useful quantum application against a classical supercomputer with the same quality target, resource boundary and current implementations. They therefore do not support a general claim that quantum computers outperform classical supercomputers. Any advantage should be described as specific to the task, implementation and baseline actually tested.
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