Robust randomized benchmarking of quantum processes
Estimate an average error rate for a set of operations (gates) on a quantum information processor, under a noise model general enough to allow errors that depend on both the time and the gate at which they occur.
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Estimate an average error rate for a set of operations (gates) on a quantum information processor, under a noise model general enough to allow errors that depend on both the time and the gate at which they occur. The paper describes a simple randomized benchmarking protocol for quantum information processors and, from a perturbative expansion of the errors, obtains a sequence of models for the observable fidelity decay. What the protocol returns is an estimate of an average error rate for a set of operations (gates), and the paper states that it is able to prove this estimate efficient and reliable under a general noise model that allows for both time- and gate-dependent errors. The paper also determines the conditions under which the estimate remains valid, and reports that it illustrates the protocol through numerical examples. The abstract stops there: it does not say what separates one model in that sequence from the next, or how an observed decay is matched against them.
Circuit & simulation
problem
encodetransform
algorithm
transformmeasure
readout
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What this takes and returns
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 →
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.
How it works
The paper describes a simple randomized benchmarking protocol for quantum information processors and, from a perturbative expansion of the errors, obtains a sequence of models for the observable fidelity decay. What the protocol returns is an estimate of an average error rate for a set of operations (gates), and the paper states that it is able to prove this estimate efficient and reliable under a general noise model that allows for both time- and gate-dependent errors. The paper also determines the conditions under which the estimate remains valid, and reports that it illustrates the protocol through numerical examples. The abstract stops there: it does not say what separates one model in that sequence from the next, or how an observed decay is matched against them. The Classiq library carries this subject under applications · benchmarking. The sources read state no complexity bound for this record (The abstract of arXiv:1009.3639, the only source read for this record, states no bound. Its cost claim is qualitative: "We are able to prove that the protocol provides an efficient and reliable estimate of an average error-rate for a set operations (gates) under a general noise model that allows for both time and gate-dependent errors" — quoted as the abstract has it, "a set operations" included. It quotes no number at all: not a count of the operations applied, not a number of repetitions or measurements, not a qubit or gate count, and no scaling in any of them; and the conditions under which the estimate remains valid are determined inside the paper rather than in the abstract. The field is therefore empty on purpose, rather than filled with a plausible bound written from memory.).
Implementation
Unsupported
randomized-benchmarking-protocol.txt
ALGORITHM: Robust randomized benchmarking of quantum processes
PROBLEM: Estimate an average error rate for a set of operations (gates) on a quantum information processor, under a noise model general enough to allow errors that depend on both the time and the gate at which they occur.
IDEA: The paper describes a simple randomized benchmarking protocol for quantum information processors and, from a perturbative expansion of the errors, obtains a sequence of models for the observable fidelity decay. What the protocol returns is an estimate of an average error rate for a set of operations (gates), and the paper states that it is able to prove this estimate efficient and reliable under a general noise model that allows for both time- and gate-dependent errors. The paper also determines the conditions under which the estimate remains valid, and reports that it illustrates the protocol through numerical examples. The abstract stops there: it does not say what separates one model in that sequence from the next, or how an observed decay is matched against them.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:1009.3639, the only source read for this record, states no bound. Its cost claim is qualitative: "We are able to prove that the protocol provides an efficient and reliable estimate of an average error-rate for a set operations (gates) under a general noise model that allows for both time and gate-dependent errors" — quoted as the abstract has it, "a set operations" included. It quotes no number at all: not a count of the operations applied, not a number of repetitions or measurements, not a qubit or gate count, and no scaling in any of them; and the conditions under which the estimate remains valid are determined inside the paper rather than in the abstract. The field is therefore empty on purpose, rather than filled with a plausible bound written from memory.
DEMONSTRATED BY: the Classiq library entry applications/benchmarking/randomized_benchmarking
PRIMARY SOURCE: Easwar Magesan, J. M. Gambetta, Joseph Emerson (2010), Robust randomized benchmarking of quantum processes — https://arxiv.org/abs/1009.3639
This is a literature reference record, not an executable circuit.
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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.
Declared gaps
Nobody has reviewed this record for gaps yet.
Literature & references
Robust randomized benchmarking of quantum processes2010 · Easwar Magesan, J. M. Gambetta, Joseph Emerson
Primary source: it describes the protocol, obtains a sequence of models for the observable fidelity decay from a perturbative expansion of the errors, and states a proof that the resulting estimate of an average error rate is efficient and reliable under a noise model allowing time- and gate-dependent errors. Consult it for how the protocol is constructed, for the conditions under which the estimate remains valid, and for the numerical examples: the abstract mentions the last two without stating either, says nothing about the first, and quotes no cost figure of any kind.