On optimum Hamiltonians for state transformations
Open accessAbstract
For a prescribed pair of quantum states |ψ I ⟩ and |ψ F ⟩ we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation |ψ I ⟩ → |ψ F ⟩ in the shortest duration. The derivation is geometric in character and does not rely on variational calculus.
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For pure states, the results of Theorem 1 also follow from the analyses presented in references 12 and 15.
“For pure states, results of Theorem1 also follow from the analyses presented in 12 and. 15”
From Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight (2009) · cites this paper as [15]
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Cites
Anandan, J., & Aharonov, Y. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.1697 · Cited by 794 · see citing works
Brody, D. C., & Hughston, L. P. (2001) · Journal of Geometry and Physics · doi:10.1016/s0393-0440(00)00052-8 · Cited by 397 · see citing works
Self-citationTime-Optimal Quantum Evolution
Carlini, A., Hosoya, A., Koike, T., & Okudaira, Y. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.060503 · Cited by 301 · see citing works
Elementary derivation for passage times
Brody, D. C. (2003) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/36/20/314 · Cited by 99 · see citing works
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Research works printed but not linked: 1
- Boscain U and Mason P 2005 Time minimal trajectories for a spin 1/2 particle in a magnetic field (Preprint quant-ph/0512074) · arXiv
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Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984 · see citing works
Faster than Hermitian quantum mechanics
Bender, C. M., Brody, D. C., Jones, H. F., & Meister, B. K. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.040403 · Cited by 417 · see citing works
Self-citationFundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight
Levitin, L. B., & Toffoli, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.160502 · Cited by 302 · see citing works
Quantum speed limit and optimal evolution time in a two-level system
Poggi, P. M., Lombardo, F. C., & Wisniacki, D. A. (2013) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/104/40005 · Cited by 70 · see citing works
Time-dependent Hamiltonians with 100% evolution speed efficiency
Uzdin, R., Günther, U., Rahav, S., & Moiseyev, N. (2012) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/45/41/415304 · Cited by 54 · see citing works
- Authors
- Brody, D. C., & Hook, D. W.
- Affiliations
- Imperial College London (GB)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2006-03-01
- Volume
- 39
- Issue
- 11
- Pages
- L167-L170
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2065894084
- Cited by
- 84
- References
- 4
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 4 · 2023: 4 · 2022: 4 · 2021: 5 · 2020: 3 · 2019: 3 · 2018: 2 · 2017: 1 · 2016: 1 · 2015: 7 · 2014: 1 · 2013: 6 · 2012: 8
- FWCI
- 4.95
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Spiral (Imperial College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Royal Society
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum state transformation, unitary transformation, eigenvalue constraints, geometric derivation, quantum control, time-optimal control
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