Russell, Benjamin James and Stepney, Susan orcid.org/0000-0003-3146-5401 (2017) The Geometry of Speed Limiting Resources in Physical Models of Computation. International Journal of Foundations of Computer Science. 321–333. ISSN 1793-6373
Abstract
We study the maximum speed of quantum computation and how it is affected by limitations on physical resources. We show how the resulting concepts generalize to a broader class of physical models of computation within dynamical systems and introduce a specific algebraic structure representing these speed limits. We derive a family of quantum speed limit results in resource-constrained quantum systems with pure states and a finite dimensional state space, by using a geometric method based on right invariant action functionals on SU(N). We show that when the action functional is bi-invariant, the minimum time for implementing any quantum gate using a potentially time-dependent Hamiltonian is equal to the minimum time when using a constant Hamiltonian, thus constant Hamiltonians are time optimal for these constraints. We give an explicit formula for the time in these cases, in terms of the resource constraint. We show how our method produces a rich family of speed limit results, of which the generalized Margolus–Levitin theorem and the Mandelstam–Tamm inequality are special cases. We discuss the broader context of geometric approaches to speed limits in physical computation, including the way geometric approaches to quantum speed limits are a model for physical speed limits to computation arising from a limited resource.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©World Scientific Publishing Company. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Computer Science (York) |
Depositing User: | Pure (York) |
Date Deposited: | 29 Aug 2017 09:45 |
Last Modified: | 16 Oct 2024 14:00 |
Published Version: | https://doi.org/10.1142/S0129054117500204 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1142/S0129054117500204 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120634 |
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