CoChat
Sign Up
Cited by 704Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Validating quantum computers using randomized model circuits

Open access
Cross, Andrew W., Bishop, Lev S., Sheldon, Sarah, Nation, Paul D., Gambetta, Jay M.·2019·Physical Review A
DOI 10.1103/physreva.100.032328
Open this paper in CoChat — free accountOpen PDF

Abstract

We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\ensuremath{\lesssim}50$), and measure it on several state-of-the-art transmon devices, finding values as high as 16. The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system. It quantifies the largest random circuit of equal width and depth that the computer successfully implements. Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes. The quantum volume is a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces quantum volume, a single-number metric measured by random model circuits of equal width and depth using heavy output generation, and reports measurements on IBM Q transmon devices with values as high as 16. It links quantum volume to system error rates, connectivity, and circuit optimization, and provides simulations for how it scales with two-qubit error and coupling map.

Key findings

  • Quantum volume is defined as \(V_Q = 2^{\min(d,m)}\), measuring the largest square-shaped model circuit a quantum computer successfully implements; measured values reach as high as 16 (\(\log_2 V_Q = 4\)). On the tested devices, \(\log_2 V_Q = 3\) for Tokyo, \(\log_2 V_Q = 2\) for Tenerife, and \(\log_2 V_Q < 2\) for Melbourne.
  • Heavy output probabilities for \(m=d\) circuits include Tokyo \(m=d=2\): 0.718(0.006), \(m=d=3\): 0.682(0.002)*, \(m=d=4\): 0.614(0.003); Johannesburg \(m=d=4\): 0.664(0.004), and optimized \(m=d=4\): 0.699(0.001), against the 2/3 threshold.
  • Circuit optimization improves performance: standard Qiskit Terra transpiler produced 28.1 CX gates on average with \(\hat h_d = 0.614(0.003)\); KAK reduced this to 21.0 CX gates with \(\hat h_d = 0.632(0.005)\); approximate SU(4) with 1% CX error used 17.7 CX gates and achieved \(\hat h_d = 0.649(0.005)\). Noisy depolarizing simulations substantially over-estimated experimental performance.
  • Connectivity simulations show all-to-all connectivity has an advantage: for \(\log_2 V_Q = 12\), the maximum permissible two-qubit error was 0.0032 for all-to-all, 0.0015 for square grid, and 0.0014 for loop. Measurement error reduces permissible two-qubit error for square grid at \(\log_2 V_Q = 12\) from 0.0015 at 0% to 0.00125 at 1% and 0.0002 at 5%.

Methods

  • The protocol uses random model circuits of width \(m\) and depth \(d\), built from layers of random permutations and Haar-random SU(4) two-qubit gates, compiled to the target device’s gate set. Success is evaluated via the heavy output generation problem, requiring heavy output probability \(h_d > 2/3\), with quantum volume defined as \(V_Q = 2^{\min(d,m)}\).
  • Experiments were run on four IBM Q devices: 5-qubit Tenerife, 16-qubit Melbourne, 20-qubit Tokyo, and 20-qubit Johannesburg. For each \(m\), 200 circuits were run for \(d=m\) with \(m \in \{2,3,4\}\); repeats used 5000 circuits for \(m=2\) on Tenerife and \(m=3\) on Tokyo, and 1000 circuits for optimized Johannesburg experiments. Results were compared with depolarizing noise simulations.
  • Simulations of all-to-all, square-grid, and loop coupling maps up to 12 qubits estimated the two-qubit gate error required for \(\log_2 V_Q = 4, 6, 8, 12\), assuming single-qubit error equal to \(\epsilon/10\) and measurement errors of 0%, 1%, and 5% for the square grid.

Limitations

  • The paper states that noisy simulations substantially over-estimate performance, that classical computation of the heavy set scales exponentially with \(m\), and that for error rates as low as \(10^{-4}\) model circuits may still be small enough to simulate classically; lower error rates may require new or modified volume metrics. It also notes that the LOCO optimization did not significantly improve heavy output generation for small numbers of qubits, and that connectivity comparisons involve small total qubit numbers, with asymptotic loop-versus-grid differences potentially larger.
  • Evident from the text: experimental validation is limited to four IBM Q transmon devices and small square circuits up to \(m=d=4\) (with \(m=d=5\) on Johannesburg), so larger-device and architecture conclusions rely on simulations. Device error rates were measured one day before the experiments and can fluctuate during the experiment timescale.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physreva.100.032328

Cites

45 of 45 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 28 cited sources checked · 0 supported · 0 flagged

  • Findingnone given
    § Validating quantum computers using randomized model circuits · p. 1

    Quantum volume is empirically reduced by uncontrolled interactions within the system.

    “The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system.”
    Quote in the paperNot a substantial claim
  • Findingown data
    § Validating quantum computers using randomized model circuits · p. 3

    The noisy simulation substantially over-estimates the performance of the devices.

    “We note that the noisy simulation substantially over-estimates the performance, highlighting the value of system-level metrics such as quantum volume.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Validating quantum computers using randomized model circuits · p. 3

    The measured heavy output probability for m=d=4 on Tokyo with the standard Qiskit Terra transpiler is 0.614(0.003).

    “the standard Qiskit Terra transpiler [ ? ] produces circuits with 28 CX gates on average, and we measure ˆ h d = 0 . 614(0 . 003); KAK reduces the average number of CX gates to 21 and produces ˆ h d = 0 . 632(0 . 005).”
    Quote in the paperSubstantial claim
  • Findingown data
    § Validating quantum computers using randomized model circuits · p. 3

    The measured heavy output probability for m=d=4 on Tokyo with the KAK decomposition is 0.632(0.005).

    “the standard Qiskit Terra transpiler [ ? ] produces circuits with 28 CX gates on average, and we measure ˆ h d = 0 . 614(0 . 003); KAK reduces the average number of CX gates to 21 and produces ˆ h d = 0 . 632(0 . 005).”
    Quote in the paperNot a substantial claim
  • Findingown data
    § Validating quantum computers using randomized model circuits · p. 3

    The standard Qiskit Terra transpiler produces circuits with 28 CX gates on average for m=d=4 on Tokyo.

    “the standard Qiskit Terra transpiler [ ? ] produces circuits with 28 CX gates on average, and we measure ˆ h d = 0 . 614(0 . 003); KAK reduces the average number of CX gates to 21 and produces ˆ h d = 0 . 632(0 . 005).”
    Quote in the paperNot a substantial claim
  • May combine two claims. 16
  • Classified as probably not a substantial claim. 23

  • May combine two claims.

    Findingown data
    § Validating quantum computers using randomized model circuits · p. 3

    Johannesburg has the lowest gate error rates of all devices measured, with single-qubit gate errors a factor of four smaller and two-qubit gate errors nearly half than those measured on Tokyo.

    “This device has the lowest gate error rates of all the devices measured, with single qubit gate errors a factor of four smaller and two qubit gate errors nearly half than those measured on Tokyo .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Validating quantum computers using randomized model circuits · p. 5

    There is little difference between the required two-qubit error rate for the square grid versus the loop graphs; the error rate for the loop is less than 7% lower than that of the square grid for the 12-qubit case.

    “At the same time, there is little difference between the required two-qubit error rate for the square grid versus the loop graphs; the error rate for the loop is less than 7% lower than that of the square grid for the 12-qubit case.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Appendix B: Approximate compiling · p. 10

    The 2-basis gate approximations have median fidelities F(2)avg = 0.99 and F(2m)avg = 0.997, comparing favorably to typical 2-qubit gate fidelities for current quantum devices.

    “The 2-basis gate approximations perform surprisingly well, with the median fidelities F (2) avg = 0 . 99, F (2 m ) avg = 0 . 997 comparing favorably to the typical 2-qubit gate fidelities for current quantum devices.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Appendix B: Approximate compiling · p. 10

    For Fb=0.97, the effective fidelities are Fe=0.976 and F(m)e=0.978, reducing infidelity by factors of 0.82 and 0.74 respectively.

    “For F b = 0 . 97 we get F e = 0 . 976, F ( m ) e = 0 . 978, reducing the infidelity by factors of 0.82 and 0.74 respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Appendix B: Approximate compiling · p. 10

    With a basis gate fidelity Fb=0.97 and no mirroring, the best expansion uses 3 applications of the basis for 22%, two applications for 76%, one application for 2%, and zero applications for <0.1% of targets, averaging 2.2 basis gate applications.

    “With a fairly noisy basis gate F b = 0 . 97 and no mirroring, the best expansion by this method has 3 applications of the basis for 22%, two applications for 76%, one application for 2%, and zero applications for &lt; 0 . 1% of targets, thus an average of 2.2 basis gate applications.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Appendix B: Approximate compiling · p. 10

    With freedom to mirror and Fb=0.97, the best expansion uses 3 applications for 3%, two applications for 93%, one application for 4%, and zero applications for <0.1% of targets, averaging 2.0 basis gate applications.

    “With the freedom to mirror, three applications for 3%, two applications for 93%, one application for 4%, and zero applications for &lt; 0 . 1% of targets, thus a mean of 2.0 basis gate applications.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § Appendix A: Qiskit transpiler passes · p. 8

    The LOCO optimization did not lead to significant improvements for heavy output generation using small numbers of qubits.

    “Although this optimization did not lead to significant improvements for heavy output generation using small numbers of qubits, we expect SWAP optimizations such as these to further improve results for larger circuits mapped onto devices with limited connectivity.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Validating quantum computers using randomized model circuits · p. 5

    The paper introduced an approximate method for NISQ devices and used it to show experimental improvements.

    “In particular, we introduced an approximate method for NISQ devices, and used it to show experimental improvements.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Validating quantum computers using randomized model circuits · p. 5

    The paper implemented various circuit optimization passes and showed a measurable change in experimental performance.

    “We implemented various circuit optimization passes (far from optimal) and showed a measurable change in the experimental performance.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 1

    Circuits with a similar form to random circuits appear in near-term algorithms like quantum adiabatic optimization algorithms and variational quantum eigensolvers.

    “In addition, circuits with a similar form appear in near-term algorithms like quantum adiabatic optimization algorithms [17] and variational quantum eigensolvers [18].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [17] source

      Not checked in the free run.

    • cites [18] J. R. McClean, J. Romero, R. Babbush, and A. AspuruGuzik, New J. Phys. 18 , 023023 (2016); M.-H. Yung, J. Casanova, A. Mezzacapo, J. McClean, L. Lamata, A. Aspuru-Guzik, and E. Solano, Sci. Rep. 4 (2014). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 1

    Random circuits are used as the basis of proposals for demonstrating quantum advantage.

    “However, random circuits model generic state preparations, and are used as the basis of proposals for demonstrating quantum advantage [16].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [16]

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 2

    Clever partitioning of circuits can achieve good parallelism and efficient use of distributed memory resources for particular supercomputer architectures.

    “Clever partitioning of circuits can achieve good parallelism and efficient use of distributed memory resources for particular supercomputer architectures [21-27].”
    Quote in the paperNot a substantial claim0 of 7 sources checked
    • cites [21] Z.-Y. Chen, Q. Zhou, C. Xue, X. Yang, G.-C. Guo, and G.-P. Guo, Science Bulletin 63 , 964 (2018), arXiv: 1802.06952. source

      Not checked in the free run.

    • cites [22] J. Chen, F. Zhang, C. Huang, M. Newman, and Y. Shi, arXiv:1805.01450 [quant-ph] (2018), arXiv: 1805.01450. source

      Not checked in the free run.

    • cites [23] R. Li, B. Wu, M. Ying, X. Sun, and G. Yang, arXiv:1804.04797 [quant-ph] (2018), arXiv: 1804.04797. source

      Not checked in the free run.

    • cites [24] E. Pednault, J. A. Gunnels, G. Nannicini, L. Horesh, T. Magerlein, E. Solomonik, and R. Wisnieff, arXiv:1710.05867 [quant-ph] (2017), arXiv: 1710.05867. source

      Not checked in the free run.

    • cites [25] S. Boixo, S. V. Isakov, V. N. Smelyanskiy, and H. Neven, arXiv:1712.05384 [quant-ph] (2017), arXiv: 1712.05384.

      Not checked in the free run.

    • cites [26] T. H¨ aner, D. S. Steiger, M. Smelyanskiy, and M. Troyer, arXiv:1604.06460 [quant-ph] (2016), arXiv: 1604.06460.

      Not checked in the free run.

    • cites [27] M. Smelyanskiy, N. P. D. Sawaya, and A. Aspuru-Guzik, arXiv:1601.07195 [quant-ph] (2016), arXiv: 1601.07195. source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisenone given
    § Validating quantum computers using randomized model circuits · p. 2

    A straightforward wave-vector propagation approach to classically simulating model quantum circuits requires exponential space and time ~2^m.

    “A straightforward wave-vector propagation approach requires exponential space and time ∼ 2 m .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 2

    The quantum volume definition differs from prior definitions and loosely coincides with the complexity of classically simulating the model circuits.

    “This definition differs from [13, 14] and loosely coincides with the complexity of classically simulating the model circuits.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [13] source

      Not checked in the free run.

    • cites [14] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given
    § Validating quantum computers using randomized model circuits · p. 2

    A Feynman algorithm for classically simulating model quantum circuits uses linear space ~dm but exponential time ~4^dm.

    “A 'Feynman' algorithm uses linear space ∼ dm but exponential time ∼ 4 dm .”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § Validating quantum computers using randomized model circuits · p. 1

    Quantum algorithms are generally not random circuits.

    “Quantum algorithms are generally not random circuits.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 2

    It is possible to trade off time and space complexity in a smooth way for classically simulating model quantum circuits.

    “It is possible to trade off time and space complexity in a smooth way [19].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [19] S. Aaronson and L. Chen, arXiv preprint arXiv:1612.05903 (2016).

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 1

    High-fidelity state preparation and readout are necessary for quantum volume.

    “High-fidelity state preparation and readout are also necessary.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 1

    Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes.

    “Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 2

    For circuits defined on a 2-dimensional square grid of qubits, the state-of-the-art classical simulation is d = 40 for a 9 × 9 grid.

    “Particular efforts for circuit partitioning and parallelism have been expended for circuits defined on a 2-dimensional square grid of qubits, where the state-of-the-art is d = 40 for a 9 × 9 grid [22].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [22] J. Chen, F. Zhang, C. Huang, M. Newman, and Y. Shi, arXiv:1805.01450 [quant-ph] (2018), arXiv: 1805.01450. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Validating quantum computers using randomized model circuits · p. 1

    Quantum algorithms can be expressed as polynomial-sized quantum circuits built from two-qubit unitary gates.

    “It is well-known that quantum algorithms can be expressed as polynomial-sized quantum circuits built from two-qubit unitary gates [15].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [15] source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 1

    The quantum volume protocol can be implemented with any universal programmable quantum computing device.

    “While we focus on transmon devices, the protocol can be implemented with any universal programmable quantum computing device.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Appendix B: Approximate compiling · p. 9

    For U_b ~ CNOT ~ U_d(π/4,0,0), 3 applications of the basis are sufficient to cover all of SU(4).

    “For U b ∼ CNOT ∼ U d ( π/ 4 , 0 , 0) it is well-known [43, 44] that 3 applications of the basis is sufficient to cover all of SU(4).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [43] F. Vatan and C. Williams, Physical Review A 69 , 032315 (2004).

      Not checked in the free run.

    • cites [44] G. Vidal and C. M. Dawson, Physical Review A 69 , 010301 (2004).

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § Validating quantum computers using randomized model circuits · p. 3

    The quantum volume is defined as V_Q = 2^{min(d,m)}.

    “Therefore, we heuristically bound the treewidth of the model circuits as min( d, m ), and since the simulation complexity grows exponentially with the treewidth, we define the quantum volume as V Q = 2 min( d,m ) .”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning
    § Appendix C: Confidence intervals for the heavy probability · p. 11

    The analysis requires a minimum of n_c = 100 circuits and uses a normal approximation to the binomial.

    “we instead require a minimum of n c = 100 circuits and make a normal approximation to the binomial”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Appendix A: Qiskit transpiler passes · p. 8

    The reordering used in LOCO is efficient, with runtime linear in the number of nonzero matrix elements.

    “This reordering is efficient, having a runtime that is linear in the number of nonzero matrix elements [39].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [39] W. M. Chan and A. George, BIT 20 , 8 (1980).

      Not checked in the free run.

  • May combine two claims.

    Premisenone given
    § Validating quantum computers using randomized model circuits · p. 5

    Typical trapped-ion systems have both two-qubit gate errors and measurement errors less than 0.01.

    “Typical trapped-ion systems have both two-qubit gate errors and measurement errors less than 0.01, which based on Table III should be sufficient to achieve log 2 V Q = 6 if not higher.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Validating quantum computers using randomized model circuits · p. 5

    For superconducting devices, coupling maps with more connectivity should produce higher quantum volume, but only if additional coupling does not also introduce larger errors.

    “Similarly, we can infer that for superconducting devices, coupling maps with more connectivity should produce higher quantum volume, but only if additional coupling does not also introduce larger errors.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data
    § Validating quantum computers using randomized model circuits · p. 5

    Although all operations must improve to increase quantum volume, the first path is to prioritize improving gate fidelity above other operations such as measurement and initialization.

    “Although all operations must improve to increase the quantum volume, the first path is to prioritize improving the gate fidelity above other operations, such as measurement and initialization.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § Appendix C: Confidence intervals for the heavy probability · p. 11

    To claim success that the heavy probability h_d exceeds 2/3 with a finite number of trials, one should set a stricter threshold t > 2/3 and require the estimated heavy probability to exceed t.

    “To be confident with a finite number of trials that the heavy probability h d exceeds 2 / 3, we should set stricter threshold t &gt; 2 / 3, requiring the estimated heavy probability ˆ h d &gt; t to claim success.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Validating quantum computers using randomized model circuits · p. 5

    The relatively small difference between square grid and loop required error rates is due to the small total number of qubits, since there is a significant asymptotic difference between loop and grid layouts.

    “This relatively small difference is due to the small total number of qubits, since there is a significant asymptotic difference between loop and grid layouts.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 5

    The quantum volume metric takes into account all relevant hardware parameters, including performance parameters (coherence, calibration errors, crosstalk, spectator errors, gate fidelity, measurement fidelity, initialization fidelity), design parameters such as connectivity and gate set, and the software behind circuit optimization.

    “This metric takes into account all relevant hardware parameters. This includes the performance parameters (coherence, calibration errors, crosstalk, spectator errors, gate fidelity, measurement fidelity, initialization fidelity) as well as the design parameters such as connectivity and gate set. It also includes the software behind the circuit optimization.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Appendix B: Approximate compiling · p. 9

    Zhang et al. give decompositions using a super controlled basis U_b ~ U_d(π/4, β_b, 0) with 3 applications for arbitrary U_t and 2 applications for restricted U_t ~ U_d(α_t, β_t, 0).

    “Zhang et al. [45] give decompositions using a more general 'super controlled' basis U b ∼ U d ( π/ 4 , β b , 0), for any β b , both an expansion with 3 applications of U b to decompose an arbitrary U t ∼ U d ( α t , β t , γ t ) and also an expansion using two applications of U b for a restricted target unitary U t ∼ U d ( α t , β t , 0), γ t = 0 for any α t , β t .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [45] Y.-S. Zhang, M.-Y. Ye, and G.-C. Guo, Physical Review A 71 , 062331 (2005).

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given
    § Validating quantum computers using randomized model circuits · p. 5

    The quantum volume is architecture-independent and can be applied to any system capable of running quantum circuits.

    “Additionally, the quantum volume is architecture-independent, and can be applied to any system that is capable of running quantum circuits.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Appendix A: Qiskit transpiler passes · p. 7

    The IBM Q systems used in this paper accept quantum circuits expressed by products of controlled-NOT (CNOT) gates and single-qubit gates.

    “The IBM Q systems used in this paper accept quantum circuits expressed by products of controlled-NOT (CNOT) gates and single-qubit gates [36].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [36] A. W. Cross, L. Bishop, J. Smolin, and J. M. Gambetta, arXiv preprint arXiv:1707.03429 (2017).

      Not checked in the free run.

35 of 35

  • The authors state this as an assumption.

    The approximation of achievable model circuit depth assumes independent stochastic errors.

    “We approximate the achievable model circuit depth ˜ d ( m ) by assuming independent stochastic errors, so that the computation fails with high probability when the model circuit volume (width times depth) satisfies”

  • The authors state this as an assumption.

    In simulations for Table III, the single-qubit gate error is equal to ε/10.

    “assuming the single-qubit gate error is equal to ϵ/ 10 (Table III).”

  • The authors state this as an assumption.

    In the Table III estimates, measurements are perfect.

    “The estimates are based on simulations using a depolarizing noise model with two-qubit error ϵ as given, single-qubit error equal to ϵ/ 10, and perfect measurements.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • These metrics all involve certain randomness due to synthetically generated inputs or circuits, which do not necessarily share the properties of real quantum workloads.

    “Besides, these metrics all involve certain randomness due to synthetically generated inputs or circuits, which do not necessarily share the properties of real quantum workloads.”

    From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [28]

    On p. 1, the paper says quantum volume uses random model circuits and that quantum algorithms are generally not random circuits. This supports the distinction from real workloads, but the paper does not establish that all the metrics referred to in the citing sentence use synthetically generated inputs or circuits. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • Cross et al. tried to validate quantum computers using randomized model circuits and attempted to introduce a method for NISQ.

    “Cross etal. tried to validate the quantum computers using randomized model circuits andhave attempted to introduce a method for NISQ [54].”

    From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [54]

  • Cross et al. defined the quantum volume protocol which quantified the largest random circuit of equal width and depth that a NISQ device can successfully implement, taking gate and measurement error into consideration.

    “Regarding QC metrics, Cross et al. deined the quantum volume protocol which quantiied the largest random circuit of equal width and depth that a NISQ device can successfully implement [28], taking gate and measurement error into consideration.”

    From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [28]

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. S. Aaronson, 2017, Proceedings of the 32nd Computational Complexity Conference (CCC '17)
  2. T. Häner, 2016, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC '16)

Cited by

Sorted by citations

Related

Authors
Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D., & Gambetta, J. M.
Affiliations
IBM Research - Thomas J. Watson Research Center (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2019-09-20
Volume
100
Issue
3
ISSN
  • 0556-2791 (ISSN-L)
  • 2469-9926
  • 2469-9934
DOI
10.1103/physreva.100.032328
OpenAlex
W2903516100
Semantic Scholar
3a9f7dda6264e4827e78230d88fea893a9d81b09
Cited by
704
References
44
Citations by year
2026: 77 · 2025: 94 · 2024: 106 · 2023: 115 · 2022: 109 · 2021: 117 · 2020: 69 · 2019: 17
FWCI
35.58
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • arXiv (Cornell University)
Funders
Army Research Office (W911NF-14-1-0124)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
quantum volume, transmon qubits, gate error rates, near-term quantum devices, quantum error correction

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review