Seddon, J.R., Regula, B., Pashayan, H. et al. (2 more authors) (2021) Quantifying quantum speedups: improved classical simulation from tighter magic monotones. PRX Quantum, 2 (1). 010345. ISSN 2691-3399
Abstract
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm’s performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators’ performance scaling. Furthermore, our monotones establish several asymptotic and nonasymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. (https://creativecommons.org/licenses/by/4.0/) Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R043825/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Jun 2022 13:20 |
Last Modified: | 08 Jun 2022 13:20 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/prxquantum.2.010345 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187733 |