Quantum volume explained

Quantum volume is a metric that measures the capabilities and error rates of a quantum computer. It expresses the maximum size of square quantum circuits that can be implemented successfully by the computer. The form of the circuits is independent from the quantum computer architecture, but compiler can transform and optimize it to take advantage of the computer's features. Thus, quantum volumes for different architectures can be compared.

The current world record for highest quantum volume is 220, accomplished by Quantinuum's H1-1 20-qubit ion trap quantum computer.[1]

Introduction

Quantum computers are difficult to compare. Quantum volume is a single number designed to show all around performance. It is a measurement and not a calculation, and takes into account several features of a quantum computer, starting with its number of qubits—other measures used are gate and measurement errors, crosstalk and connectivity.[2] [3] [4]

IBM defined its Quantum Volume metric[5] because a classical computer's transistor count and a quantum computer's quantum bit count aren't the same. Qubits decohere with a resulting loss of performance so a few fault tolerant bits are more valuable as a performance measure than a larger number of noisy, error-prone qubits.[6] [7]

Generally, the larger the quantum volume, the more complex the problems a quantum computer can solve.[8]

Alternative benchmarks, such as Cross-entropy benchmarking, reliable Quantum Operations per Second (rQOPS) proposed by Microsoft, Circuit Layer Operations Per Second (CLOPS) proposed by IBM and IonQ's Algorithmic Qubits, have also been proposed.[9] [10]

Definition

Original Definition

The quantum volume of a quantum computer was originally defined in 2018 by Nikolaj Moll et al.[11] However, since around 2021 that definition has been supplanted by IBM's 2019 redefinition.[12] [13] The original definition depends on the number of qubits as well as the number of steps that can be executed, the circuit depth

\tilde{V}Q=min[N,d(N)]2.

The circuit depth depends on the effective error rate as

d\simeq

1
N\varepsiloneff

.

The effective error rate is defined as the average error rate of a two-qubit gate. If the physical two-qubit gates do not have all-to-all connectivity, additional SWAP gates may be needed to implement an arbitrary two-qubit gate and, where is the error rate of the physical two-qubit gates. If more complex hardware gates are available, such as the three-qubit Toffoli gate, it is possible that .

The allowable circuit depth decreases when more qubits with the same effective error rate are added. So with these definitions, as soon as, the quantum volume goes down if more qubits are added. To run an algorithm that only requires qubits on an -qubit machine, it could be beneficial to select a subset of qubits with good connectivity. For this case, Moll et al. give a refined definition of quantum volume.

VQ=maxn<N\left\{min\left[n,

1
n\varepsiloneff(n)

\right]2\right\},

where the maximum is taken over an arbitrary choice of qubits.

IBM's redefinition

In 2019, IBM's researchers modified the quantum volume definition to be an exponential of the circuit size, stating that it corresponds to the complexity of simulating the circuit on a classical computer:[14]

log2VQ=\underset{n\leN}{\operatorname{argmax}}\left\{min\left[n,d(n)\right]\right\}

Achievement history

Date Quantum
volume 		Qubit
count 		Manufacturer System name and reference
2020, January 2 28 IBM "Raleigh"[15]
2020, June 2 6 Honeywell [16]
2020, August 2 27 IBM Falcon r4 "Montreal"[17]
2020, November 2 10 Honeywell "System Model H1"[18]
2020, December 2 27 IBM Falcon r4 "Montreal"[19]
2021, March 2 10 Honeywell "System Model H1"[20]
2021, July210 Honeywell"Honeywell System H1"[21]
2021, December212 Quantinuum
(previously Honeywell)		"Quantinuum System Model H1-2"[22]
2022, April227 IBMFalcon r10 "Prague"[23]
2022, April212 Quantinuum"Quantinuum System Model H1-2"[24]
2022, May227 IBMFalcon r10 "Prague"[25]
2022, September220 Quantinuum"Quantinuum System Model H1-1"[26]
2023, February224 Alpine Quantum Technologies"Compact Ion-Trap Quantum Computing Demonstrator"[27]
2023, February220 Quantinuum"Quantinuum System Model H1-1"[28]
2023, May232 Quantinuum"Quantinuum System Model H2"[29]
2023, June220 Quantinuum"Quantinuum System Model H1-1"[30]
2024, April220Quantinuum"Quantinuum System Model H1-1"

Volumetric benchmarks

The quantum volume benchmark defines a family of square circuits, whose number of qubits and depth are the same. Therefore, the output of this benchmark is a single number. However, a proposed generalization is the volumetric benchmark[31] framework, which defines a family of rectangular quantum circuits, for which and are uncoupled to allow the study of time/space performance trade-offs, thereby sacrificing the simplicity of a single-figure benchmark.

Volumetric benchmarks can be generalized not only to account for uncoupled and dimensions, but also to test different types of quantum circuits. While quantum volume benchmarks the quantum computer's ability to implement a specific type of randomized circuits, these can, in principle, be substituted by other families of random circuits, periodic circuits,[32] or algorithm-inspired circuits. Each benchmark must have a success criterion that defines whether a processor has "passed" a given test circuit.

While these data can be analyzed in many ways, a simple method of visualization is illustrating the Pareto front of the versus trade-off for the processor being benchmarked. This Pareto front provides information on the largest depth a patch of a given number of qubits can withstand, or, alternatively, the biggest patch of qubits that can withstand executing a circuit of given depth .

See also

References

  1. Web site: Quantinuum extends its significant lead in quantum computing, achieving historic milestones for hardware fidelity and Quantum Volume . 2024-04-17 . www.quantinuum.com . en.
  2. Web site: Honeywell claims to have built the highest-performing quantum computer available. 2020-06-22. phys.org. en.
  3. Web site: Smith-Goodson. Paul. Quantum Volume: A Yardstick To Measure The Performance Of Quantum Computers. 2020-06-22. Forbes. en.
  4. Web site: Measuring Quantum Volume. 2020-08-21. Qiskit.org. en.
  5. Cross . Andrew W. . Bishop . Lev S. . Sheldon . Sarah . Nation . Paul D. . Gambetta . Jay M. . 2019 . Validating quantum computers using randomized model circuits . Phys. Rev. A . 100 . 3 . 032328 . 10.1103/PhysRevA.100.032328 . 2020-10-02. 1811.12926 . 2019PhRvA.100c2328C . 119408990 .
  6. Web site: Mandelbaum. Ryan F.. 2020-08-20. What Is Quantum Volume, Anyway?. 2020-08-21. Medium Qiskit. en.
  7. Web site: Sanders. James. 2:00 Pm. August 12, 2019. Why quantum volume is vital for plotting the path to quantum advantage. 2020-08-22. TechRepublic. en.
  8. Web site: Patty. Lee. 2020. Chief Scientist for Honeywell Quantum Solutions. Quantum Volume: The Power of Quantum Computers. 2020-08-21. www.honeywell.com. en.
  9. Web site: Yirka . Bob. 2023-06-24. Microsoft claims to have achieved first milestone in creating a reliable and practical quantum computer . 2024-07-01. phys.org. en.
  10. Web site: Leprince-Ringuet . Daphne. 2021-11-02. Quantum computing: IBM just created this new way to measure the speed of quantum processors. 2024-07-01. ZDNet. en.
  11. Nikolaj . Moll. Panagiotis . Barkoutsos. Lev S . Bishop. Jerry M . Chow. Andrew . Cross. Daniel J . Egger. Stefan . Filipp. Andreas . Fuhrer. Jay M . Gambetta. Marc . Ganzhorn. Abhinav . Kandala. Antonio . Mezzacapo. Peter . Müller. Walter . Riesswe introd. Gian . Salis. John . Smolin. Ivano . Tavernelli. Kristan . Temme. Quantum optimization using variational algorithms on near-term quantum devices. Quantum Science and Technology. 3. 2018. 3. 030503. 10.1088/2058-9565/aab822. 1710.01022. 2018QS&T....3c0503M. free.
  12. Baldwin . Charles . Mayer . Karl . 2022 . Re-examining the quantum volume test: Ideal distributions, compiler optimizations, confidence intervals, and scalable resource estimations . . 6 . 707 . 10.22331/q-2022-05-09-707 . 2110.14808 . 2022Quant...6..707B . 240070758 .
  13. Miller . Keith . 2022-07-14 . An Improved Volumetric Metric for Quantum Computers via more Representative Quantum Circuit Shapes . quant-ph . 2207.02315.
  14. https://pennylane.ai/qml/demos/quantum_volume.html (archived)
  15. Web site: IBM Doubles Its Quantum Computing Power Again. Forbes. 2020-01-08.
  16. Web site: Honeywell Claims It Has Most Powerful Quantum Computer. IEEE Spectrum. 2020-06-24. Samuel K. Moore.
  17. Web site: Condon. Stephanie. August 20, 2020. IBM hits new quantum computing milestone. 2020-08-21. ZDNet. en.
  18. Web site: Rapid Scale-Up of Commercial Ion-Trap Quantum Computers. 2020-11-10. Samuel K. Moore. IEEE Spectrum.
  19. Gambetta . Jay . Jay Gambetta . jaygambetta . 1334526177642491904 . 2020-12-03 . On the same system (IBM Q System One - Montreal) that we hit a quantum volume of 64 the team recently achieved a quantum volume of 128. This year's progress in the quality of quantum circuits has been amazing. https://t.co/pBYmLkmSoS . en . 2022-12-04 . https://web.archive.org/web/20221021003459/http://twitter.com/jaygambetta/status/1334526177642491904 . 2022-10-21 . live.
  20. Web site: Leprince-Ringuet. Daphne. Quantum computing: Honeywell just quadrupled the power of its computer. 2021-03-11. ZDNet. en.
  21. Web site: Honeywell and Cambridge Quantum Reach New Milestones. 2021-07-23. www.honeywell.com. en-US.
  22. Web site: Demonstrating Benefits of Quantum Upgradable Design Strategy: System Model H1-2 First to Prove 2,048 Quantum Volume. 2022-01-04. www.quantinuum.com. en.
  23. Web site: Pushing quantum performance forward with our highest quantum volume yet . IBM Research Blog . en . 6 April 2022.
  24. Web site: Quantinuum Announces Quantum Volume 4096 Achievement. 2022-04-14. www.quantinuum.com. en.
  25. Gambetta . Jay . Jay Gambetta . jaygambetta . 1529489786242744320 . 2022-05-25 . Just a little update from the IBM Quantum team. QV of 512 achieved. Our new gate architecture (Falcon R10) continues to allow higher fidelity and low crosstalk and as a result better quality circuits. Two jumps in QV in the last 2 months. https://t.co/szAKCAD4gA . en . 2022-12-04 . https://web.archive.org/web/20220528065407/https://twitter.com/jaygambetta/status/1529489786242744320 . 2022-05-28 . live.
  26. Web site: Quantinuum Is On A Roll – 17 Significant Quantum Computing Achievements In 12 Months . Smith-Goodson . Paul . 2022-10-06 . . 2023-02-24 . 2022-10-06 . https://web.archive.org/web/20221006170105/https://www.forbes.com/sites/moorinsights/2022/10/06/quantinuum-is-on-a-roll--17-significant-quantum-computing-achievements-in-12-months/ . bot: unknown .
  27. Web site: State of Quantum Computing in Europe: AQT pushing performance with a Quantum Volume of 128 . Monz. Thomas . 2023-02-10. techmonitor.ai . 2023-05-09.
  28. Web site: Quantinuum hits quantum performance milestone . Morrison . Ryan . 2023-02-23. techmonitor.ai . 2023-02-24.
  29. A Race-Track Trapped-Ion Quantum Processor . Moses . S.A. . Physical Review X . 2023-05-09 . 13 . 4 . 041052 . 10.1103/PhysRevX.13.041052 . 2305.03828 . 2023PhRvX..13d1052M .
  30. Web site: Quantinuum H-Series quantum computer accelerates through 3 more performance records for quantum volume . Morrison . Ryan . 2023-06-30. quantinuum . 2023-06-30.
  31. Blume-Kohout . Robin . Young . Kevin C. . A volumetric framework for quantum computer benchmarks . Quantum . 4 . 2020-11-15 . 2521-327X . 10.22331/q-2020-11-15-362 . 362. 1904.05546 . 2020Quant...4..362B .
  32. Proctor . Timothy . Rudinger . Kenneth . Young . Kevin . Nielsen . Erik . Blume-Kohout . Robin . Measuring the capabilities of quantum computers . Nature Physics . Springer Science and Business Media LLC . 18 . 1 . 2021-12-20 . 1745-2473 . 10.1038/s41567-021-01409-7 . 75–79. 2008.11294 .

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