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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.
Original language | English |
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Article number | 052403 |
Pages (from-to) | 052403-1-052403-14 |
Number of pages | 14 |
Journal | Physical Review A: covering atomic, molecular, and optical physics and quantum information |
Volume | 108 |
Issue number | 5 |
DOIs | |
Publication status | Published - Nov 2023 |
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Dive into the research topics of 'Exact and lower bounds for the quantum speed limit in finite-dimensional systems'. Together they form a unique fingerprint.Projects
- 2 Finished
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UTS led: Pushing the digital limits in quantum simulation for advanced manufacturing
Langford, N., Dehollain, J., Burgarth, D., Berry, D. & Heyl, M.
26/03/21 → 25/03/24
Project: Research
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