Algorithms · Quantum benchmarking protocol
Quantum volume from randomized model circuits
Measure, as a single number, how large a random circuit of equal width and depth a given quantum computer successfully implements, so that progress toward improved system-wide gate error rates can be measured and compared across near-term devices.
Attested & literatureUpdated
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- Record typeLiterature reference
- Reference implementationquantum_volume
- Reported costNot stated by the sources read
- Papers1
Measure, as a single number, how large a random circuit of equal width and depth a given quantum computer successfully implements, so that progress toward improved system-wide gate error rates can be measured and compared across near-term devices. Cross, Bishop, Sheldon, Nation and Gambetta introduce quantum volume, a single-number metric that can be measured using a concrete protocol on near-term quantum computers of modest size (n ≲ 50). It quantifies the largest random circuit of equal width and depth that the computer successfully implements, so a device raises its score only by handling greater width and greater depth together: the authors call it a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments. The paper links the quantum volume to system error rates, states that it is empirically reduced by uncontrolled interactions within the system, and names the system properties expected to come with higher quantum volumes — high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains. The authors report measuring the metric on several state-of-the-art transmon devices and finding values as high as 16.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Cross, Bishop, Sheldon, Nation and Gambetta introduce quantum volume, a single-number metric that can be measured using a concrete protocol on near-term quantum computers of modest size (n ≲ 50). It quantifies the largest random circuit of equal width and depth that the computer successfully implements, so a device raises its score only by handling greater width and greater depth together: the authors call it a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments. The paper links the quantum volume to system error rates, states that it is empirically reduced by uncontrolled interactions within the system, and names the system properties expected to come with higher quantum volumes — high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains. The authors report measuring the metric on several state-of-the-art transmon devices and finding values as high as 16. The sources read state no complexity bound for this record (The abstract of arXiv:1811.12926 states no cost, running time or speedup bound, and correctly so: quantum volume is a figure of merit for a device, not an algorithm with a complexity. What it states instead is a definition — "It quantifies the largest random circuit of equal width and depth that the computer successfully implements" — and a measurement, quoted here in two pieces: "We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size" and "and measure it on several state-of-the-art transmon devices, finding values as high as 16." Both pieces are verbatim; what falls between them is the size regime, which the abstract writes as TeX and which this record renders in Unicode as n ≲ 50, so it is stated outside the quotation marks rather than inside them. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with a bound written from memory.).
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Record type
- Literature reference
- Reference implementation
- quantum_volume
- Reported cost
- Not stated by the sources read
- Complexity basis
- The abstract of arXiv:1811.12926 states no cost, running time or speedup bound, and correctly so: quantum volume is a figure of merit for a device, not an algorithm with a complexity. What it states instead is a definition — "It quantifies the largest random circuit of equal width and depth that the computer successfully implements" — and a measurement, quoted here in two pieces: "We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size" and "and measure it on several state-of-the-art transmon devices, finding values as high as 16." Both pieces are verbatim; what falls between them is the size regime, which the abstract writes as TeX and which this record renders in Unicode as n ≲ 50, so it is stated outside the quotation marks rather than inside them. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with a bound written from memory.
- Circuit
- Not supplied
This record is not a concrete circuit.
Quantum vs classical
Classical baseline
Compare Quantum benchmarking protocol with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Nobody has reviewed this record for gaps yet.
ALGORITHM: Quantum volume from randomized model circuits
PROBLEM: Measure, as a single number, how large a random circuit of equal width and depth a given quantum computer successfully implements, so that progress toward improved system-wide gate error rates can be measured and compared across near-term devices.
IDEA: Cross, Bishop, Sheldon, Nation and Gambetta introduce quantum volume, a single-number metric that can be measured using a concrete protocol on near-term quantum computers of modest size (n ≲ 50). It quantifies the largest random circuit of equal width and depth that the computer successfully implements, so a device raises its score only by handling greater width and greater depth together: the authors call it a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments. The paper links the quantum volume to system error rates, states that it is empirically reduced by uncontrolled interactions within the system, and names the system properties expected to come with higher quantum volumes — high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains. The authors report measuring the metric on several state-of-the-art transmon devices and finding values as high as 16.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:1811.12926 states no cost, running time or speedup bound, and correctly so: quantum volume is a figure of merit for a device, not an algorithm with a complexity. What it states instead is a definition — "It quantifies the largest random circuit of equal width and depth that the computer successfully implements" — and a measurement, quoted here in two pieces: "We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size" and "and measure it on several state-of-the-art transmon devices, finding values as high as 16." Both pieces are verbatim; what falls between them is the size regime, which the abstract writes as TeX and which this record renders in Unicode as n ≲ 50, so it is stated outside the quotation marks rather than inside them. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with a bound written from memory.
PRIMARY SOURCE: Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta (2018), Validating quantum computers using randomized model circuits — https://arxiv.org/abs/1811.12926
This is a literature reference record, not an executable circuit.A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.
Where this sits
This record is named by the layer graph at:
- Quantum volume from random square circuits Method
Takes A programmable device — its qubits, its native gate set, its connectivity and its measurement — plus how many circuits and how many shots you are willing to spend, and the confidence level the answer has to be established at. Returns A number characterising the hardware, the protocol that produced it, and the statistical confidence it holds at — never an answer to a computational problem, because no computational problem was posed.
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References
- Validating quantum computers using randomized model circuits
Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta · 2018
Primary source: it introduces the quantum volume metric, states that it can be measured by a concrete protocol on near-term computers of modest size (n ≲ 50), defines it as the largest random circuit of equal width and depth the computer successfully implements, links it to system error rates, and reports measured values as high as 16 on several state-of-the-art transmon devices. Consult it for the protocol itself — the model circuits, the success criterion, the number of circuits and the confidence level — none of which the abstract states.