Bravyi, S., Browne, D., Calpin, P. et al. (3 more authors) (2019) Simulation of quantum circuits by low-rank stabilizer decompositions. Quantum, 3. ISSN 2521-327X
Abstract
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a pure state ψ is defined to be the smallest integer χ such that ψ is a superposition of χ stabilizer states.
Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art. A new feature is the capability to simulate circuits composed of Clifford gates and arbitrary diagonal gates, extending the reach of a previous algorithm specialized to the Clifford+T gate set. We implemented the new simulation methods and used them to simulate quantum algorithms with 40-50 qubits and over 60 non-Clifford gates, without resorting to high-performance computers. We report a simulation of the Quantum Approximate Optimization Algorithm in which we process superpositions of χ ∼ 106 stabilizer states and sample from the full n-bit output distribution, improving on previous simulations which used ∼ 103 stabilizer states and sampled only from single-qubit marginals. We also simulated instances of the Hidden Shift algorithm with circuits including up to 64 T gates or 16 CCZ gates; these simulations showcase the performance gains available by optimizing the decomposition of a circuit’s non-Clifford components.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Author(s). This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (https://creativecommons.org/licenses/by/4.0/) license. |
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 (EPSRC) EP/M024261/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Sep 2019 14:54 |
Last Modified: | 12 Sep 2019 14:54 |
Status: | Published |
Publisher: | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
Refereed: | Yes |
Identification Number: | 10.22331/q-2019-09-02-181 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150621 |