Ouyang, Y. orcid.org/0000-0003-1115-0074, White, D.R. orcid.org/0000-0001-6317-4348 and Campbell, E.T. (2020) Compilation by stochastic Hamiltonian sparsification. Quantum, 4. p. 235. ISSN 2521-327X
Abstract
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2020 The Authors. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | quant-ph; quant-ph |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R043825/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 04 May 2023 13:22 |
Last Modified: | 04 May 2023 13:22 |
Published Version: | http://dx.doi.org/10.22331/q-2020-02-27-235 |
Status: | Published |
Publisher: | Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften |
Refereed: | Yes |
Identification Number: | 10.22331/q-2020-02-27-235 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198719 |