Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 052403 |
| Seitenumfang | 14 |
| Fachzeitschrift | Physical Review A |
| Jahrgang | 108 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - 2 Nov. 2023 |
Abstract
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups, and differential geometry and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally, we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Atom- und Molekularphysik sowie Optik
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in: Physical Review A, Jahrgang 108, Nr. 5, 052403, 02.11.2023.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Exact and lower bounds for the quantum speed limit in finite-dimensional systems
AU - Johnsson, Mattias T.
AU - Van Luijk, Lauritz
AU - Burgarth, Daniel
N1 - Funding Information: We thank the anonymous referees for their kind remarks and useful suggestions. D.B. acknowledges funding from the Australian Research Council (Project No. FT190100106, No. DP210101367, and No. CE170100009).
PY - 2023/11/2
Y1 - 2023/11/2
N2 - A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups, and differential geometry and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally, we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.
AB - A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups, and differential geometry and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally, we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.
UR - http://www.scopus.com/inward/record.url?scp=85176124576&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2304.06617
DO - 10.48550/arXiv.2304.06617
M3 - Article
AN - SCOPUS:85176124576
VL - 108
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 5
M1 - 052403
ER -