Quantum volume

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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.

In 2020, the highest achieved quantum volume (per § IBM's modified definition) rose from 32 for IBM's computer "Raleigh"[1] to 128 for Honeywell's "H1",[2] i.e. quantum circuits of size up to 7×7 have been implemented successfully. More recently in 2021, Honeywell's "H1",[2] first achieved a measured quantum volume of 512.[3], and within six months doubled that performance to 1024.[4]


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.[5][6][7]

IBM introduced the Quantum Volume metric [8] 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.[9][10]

Generally, the larger the quantum volume, the more complex the problems a quantum computer can solve.[11]


The quantum volume of a quantum computer is defined by Nikolaj Moll et al.[12] It depends on the number of qubits N as well as the number of steps that can be executed, the circuit depth d

The circuit depth depends on the effective error rate as

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 N-qubit machine, it could be beneficial to select a subset of qubits with good connectivity. For this case, Moll et al. [12] give a refined definition of quantum volume.

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

IBM's modified definition[edit]

The 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:[8][13]

Algorithmic Qubits (AQ)[edit]

Algorithmic Qubits is the level equivalent of quantum volume, introduced by IonQ, and defined as .[14]

IonQ announced a quantum computer with a claimed AQ of 22 (quantum volume of 4,194,304) in October 2020,[15] although these numbers have not been empirically verified.

Achievement history[edit]

Date Quantum volume[a]
(circuit size)
Manufacturer Notes
2020, January 32 (5×5) IBM "Raleigh" (28 qubits)[1]
2020, June 64 (6×6) Honeywell 6 qubits[16]
2020, August 64 (6×6) IBM Falcon r4 "Montreal" (27 qubits)[17]
2020, November 128 (7×7) Honeywell "System Model H1" (10 qubits)[2]
2020, December 128 (7×7) IBM Falcon r4 "Montreal" (27 qubits)[18]
2021, March 512 (9×9) Honeywell "System Model H1" (10 qubits)[19]
2021, July 1024 (10x10) Honeywell "Honeywell System H1" (10 qubits) [20]
2021, December 2048 (11x11) Quantinuum (previously Honeywell) "Quantinuum System Model H1-2" (12 qubits) [21]
2022, April 256 (8×8) IBM Falcon r10 "Prague" (27 qubits) [22]
2022, April 4096 (12x12) Quantinuum (previously Honeywell) "Quantinuum System Model H1-2" (12 qubits) [23]
2022, May 512 (9×9) IBM Falcon r10 "Prague" (27 qubits) [24]

See also[edit]


  1. ^ a b "IBM Doubles Its Quantum Computing Power Again". Forbes. 2020-01-08.
  2. ^ a b c Samuel K. Moore (2020-11-10). "Rapid Scale-Up of Commercial Ion-Trap Quantum Computers". IEEE Spectrum.
  3. ^ "Honeywell Sets New Record For Quantum Computing Performance". Honeywell, Inc. Retrieved 2021-04-05.
  4. ^ "Quantum Milestone 16 fold Increase in Performance in a Year". Honeywell, Inc. Retrieved 2021-09-22.
  5. ^ "Honeywell claims to have built the highest-performing quantum computer available". phys.org. Retrieved 2020-06-22.
  6. ^ Smith-Goodson, Paul. "Quantum Volume: A Yardstick To Measure The Performance Of Quantum Computers". Forbes. Retrieved 2020-06-22.
  7. ^ "Measuring Quantum Volume". Qiskit.org. Retrieved 2020-08-21.{{cite web}}: CS1 maint: url-status (link)
  8. ^ a b 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. arXiv:1811.12926. Bibcode:2019PhRvA.100c2328C. doi:10.1103/PhysRevA.100.032328. S2CID 119408990. Retrieved 2020-10-02.
  9. ^ Mandelbaum, Ryan F. (2020-08-20). "What Is Quantum Volume, Anyway?". Medium Qiskit. Retrieved 2020-08-21.{{cite web}}: CS1 maint: url-status (link)
  10. ^ Sanders, James (August 12, 2019). "Why quantum volume is vital for plotting the path to quantum advantage". TechRepublic. Retrieved 2020-08-22.{{cite web}}: CS1 maint: url-status (link)
  11. ^ Patty, Lee (2020). "Quantum Volume: The Power of Quantum Computers". www.honeywell.com. Chief Scientist for Honeywell Quantum Solutions. Retrieved 2020-08-21.{{cite web}}: CS1 maint: url-status (link)
  12. ^ a b Moll, Nikolaj; Barkoutsos, Panagiotis; Bishop, Lev S; Chow, Jerry M; Cross, Andrew; Egger, Daniel J; Filipp, Stefan; Fuhrer, Andreas; Gambetta, Jay M; Ganzhorn, Marc; Kandala, Abhinav; Mezzacapo, Antonio; Müller, Peter; Riesswe introd, Walter; Salis, Gian; Smolin, John; Tavernelli, Ivano; Temme, Kristan (2018). "Quantum optimization using variational algorithms on near-term quantum devices". Quantum Science and Technology. 3 (3): 030503. arXiv:1710.01022. Bibcode:2018QS&T....3c0503M. doi:10.1088/2058-9565/aab822.
  13. ^ https://pennylane.ai/qml/demos/quantum_volume.html (archived)
  14. ^ "Scaling IonQ's Quantum Computers: The Roadmap".
  15. ^ "Introducing the World's Most Powerful Quantum Computer".
  16. ^ Samuel K. Moore (2020-06-24). "Honeywell Claims It Has Most Powerful Quantum Computer". IEEE Spectrum.
  17. ^ Condon, Stephanie (August 20, 2020). "IBM hits new quantum computing milestone". ZDNet. Retrieved 2020-08-21.{{cite web}}: CS1 maint: url-status (link)
  18. ^ Twitter https://twitter.com/jaygambetta/status/1334526177642491904. {{cite web}}: Missing or empty |title= (help)
  19. ^ Leprince-Ringuet, Daphne. "Quantum computing: Honeywell just quadrupled the power of its computer". ZDNet. Retrieved 2021-03-11.
  20. ^ "Honeywell and Cambridge Quantum Reach New Milestones". www.honeywell.com. Retrieved 2021-07-23.
  21. ^ "Demonstrating Benefits of Quantum Upgradable Design Strategy: System Model H1-2 First to Prove 2,048 Quantum Volume". www.quantinuum.com. Retrieved 2022-01-04.
  22. ^ "Pushing quantum performance forward with our highest quantum volume yet". IBM Research Blog. 6 April 2022.
  23. ^ "Quantinuum Announces Quantum Volume 4096 Achievement". www.quantinuum.com. Retrieved 2022-04-14.
  24. ^ Jay Gambetta on Twitter https://twitter.com/jaygambetta/status/1529489786242744320. {{cite web}}: Missing or empty |title= (help)