Exact and lower bounds for the quantum speed limit in finite-dimensional systems
Johnsson MT, Van Luijk L, Burgarth D (2023)
Publication Type: Journal article
Publication year: 2023
Journal
Book Volume: 108
Article Number: 052403
Journal Issue: 5
DOI: 10.1103/PhysRevA.108.052403
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.
Involved external institutions
Australia (AU)
Germany (DE)How to cite
APA:
Johnsson, M.T., Van Luijk, L., & Burgarth, D. (2023). Exact and lower bounds for the quantum speed limit in finite-dimensional systems. Physical Review A, 108(5). https://dx.doi.org/10.1103/PhysRevA.108.052403
MLA:
Johnsson, Mattias T., Lauritz Van Luijk, and Daniel Burgarth. "Exact and lower bounds for the quantum speed limit in finite-dimensional systems." Physical Review A 108.5 (2023).
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