Randomized benchmarking of quantum gates
Open accessAbstract
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized $\ensuremath{\pi}/2$ pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.
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The paper gives a full analysis of the scalable multi-qubit randomized benchmarking protocol for Clifford gates proposed in [25] which overcomes the shortcomings described above.
“In this paper we give a full analysis of the scalable multi-qubit randomized benchmarking protocol for Clifford gates we proposed in [25] which overcomes the shortcomings described above.”
From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [25]
Gate-dependent errors can lead to a deviation from the exponential decay, defining a partial test for such effects in the noise.
“The fitting formula shows that gatedependent errors can lead to a deviation from the exponential decay (defining a partial test for such effects in the noise), which was illustrated via numerical examples in [25].”
From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [25]
There exist physically relevant noise models for which, when the true value of the depolarization fidelity parameter p is used, the first-order model fits the experimental data much better than the zeroth-order model.
“As depicted in [25] there exist physically relevant noise models for which when the true value of the depolarization fidelity parameter p is used, the first order model fits the experimental data much better than the zeroth order model.”
From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [25]
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- Authors
- Knill, E., Leibfried, D., Reichle, R., Britton, J., Blakestad, R. B., Jost, J. D., Langer, C., Ozeri, R., Seidelin, S., & Wineland, D. J.
- Affiliations
- National Institute of Standards and Technology (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-01-08
- Volume
- 77
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2170620327
- Cited by
- 1,019
- References
- 27
- Citations by year
- 2026: 67 · 2025: 118 · 2024: 99 · 2023: 122 · 2022: 85 · 2021: 121 · 2020: 94 · 2019: 70 · 2018: 41 · 2017: 39 · 2016: 43 · 2015: 31 · 2014: 25 · 2013: 16 · 2012: 12
- FWCI
- 18.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- APS
- 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 Mechanics and Applications
- Keywords
- randomized benchmarking, quantum gate errors, quantum computing scalability, state preparation and measurement errors
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