Time-optimal unitary operations
Open accessAbstract
Extending our previous work on time-optimal quantum state evolution [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)], we formulate a variational principle for finding the time-optimal realization of a target unitary operation, when the available Hamiltonians are subject to certain constraints dictated either by experimental or by theoretical conditions. Since the time-optimal unitary evolutions do not depend on the input quantum state this is of more direct relevance to quantum computation. We explicitly illustrate our method by considering the case of a two-qubit system self-interacting via an anisotropic Heisenberg Hamiltonian and by deriving the time-optimal unitary evolution for three examples of target quantum gates, namely, the swap of qubits, the quantum Fourier transform, and the entangler gate. We also briefly discuss the case in which certain unitary operations take negligible time.
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Together with the Schrödinger equation, the quantum brachistochrone equation defines a nonlinear ordinary differential boundary-value problem with U(0)=I and U(T)=V.
“Together with the Schrödinger equation, the QBE [Eq.( 1)] defines a boundary value problem for a nonlinear ODE, with the boundary values Uð0Þ ¼ I and UðTÞ ¼ V.”
From Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems (2015) · cites this paper as [28]
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References 20 · Cited by 126
Research works printed but not linked: 1
- [16]P.W. Shor, Proc. 35th Ann. Sym. Found. Comp. Sci. , 124 (IEEE Computer Society Press, New York, 1994).
- Authors
- Carlini, A., Hosoya, A., Koike, T., & Okudaira, Y.
- Affiliations
- Tokyo Institute of Technology (JP)
- Keio University (JP)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-04-10
- Volume
- 75
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2043010374
- Cited by
- 126
- References
- 20
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 6 · 2023: 6 · 2022: 6 · 2021: 8 · 2020: 7 · 2019: 9 · 2018: 5 · 2017: 7 · 2016: 5 · 2015: 16 · 2014: 4 · 2013: 8 · 2012: 4
- FWCI
- 7.10
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Tokyo Tech Research Repository (Tokyo Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- 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
- time-optimal control, unitary operations, variational principle, quantum state evolution, two-qubit systems, quantum gates, quantum Fourier transform, entangling gates, quantum computing
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