Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control
Open accessAbstract
We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit perfect entanglers. We find that this volume corresponds to more than 84% of the total invariant volume of the space of two-qubit gates. This same metric is also used to determine the effective target sizes that selected gates will present in any quantum-control procedure designed to implement them.
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Recently, trapped-ion experiments have demonstrated two-qubit gates with errors of 0.001.
“Recently, trapped-ion experiments have demonstrated two-qubit gates with errors of 0.001 [34], indicating higher quantum volumes should be possible.”
From Validating quantum computers using randomized model circuits (2019) · cites this paper as [34]
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References 13 · Cited by 31
Research works printed but not linked: 1
- Mehta, M.L. Random Matrices, 2nd ed.; Academic Press: New York, NY, USA, 1991.
- Authors
- Watts, P., O'Connor, M., & Vala, J.
- Affiliations
- Dublin Institute For Advanced Studies (IE)
- National University of Ireland, Maynooth (IE)
- Corresponding author
- Vala, Jiří
- Venue
- Entropy
- Publisher
- MDPI AG
- Published
- 2013-05-23
- Volume
- 15
- Issue
- 6
- Pages
- 1963-1984
- ISSN
- 1099-4300 (ISSN-L)
- OpenAlex
- W2030523291
- Cited by
- 31
- References
- 13
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 4 · 2023: 4 · 2022: 5 · 2021: 2 · 2019: 7 · 2018: 2 · 2015: 3
- FWCI
- 1.11
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Entropy (publishedVersion, cc-by)
- Maynooth University ePrints and eTheses Archive (Maynooth University) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Science Foundation Ireland (10/IN.1/I3013, Principal Investigator Award 10/IN.1/I3013)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- two-qubit gates, compact Lie groups, quantum control, target size, entanglement, quantum information processing
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