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arXiv · 2304.06617

Exact and lower bounds for the quantum speed limit in finite dimensional systems

Mattias T. Johnsson·Lauritz van Luijk·Daniel Burgarth
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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.

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Mattias T. Johnsson, Lauritz van Luijk, Daniel Burgarth. 2023-04-13. Exact and lower bounds for the quantum speed limit in finite dimensional systems. https://doi.org/10.1103/physreva.108.052403

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