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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2022.5
URN: urn:nbn:de:0030-drops-165128
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16512/
Kissinger, Aleks ;
van de Wetering, John ;
Vilmart, Renaud
Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions
Abstract
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser entangled states which have more favourable decompositions, we can speed up these simulations. This is made possible by using the ZX-calculus, which allows us to easily find instances of these entangled states in the simplified diagram representing the quantum circuit to be simulated. We additionally find a new technique of partial stabiliser decompositions that allow us to trade magic states for stabiliser terms. With this technique we require only 2^{α t} stabiliser terms, where α≈ 0.396, to simulate a circuit with T-count t. This matches the α found by Qassim et al. [Qassim et al., 2021], but whereas they only get this scaling in the asymptotic limit, ours applies for a circuit of any size. Our method builds upon a recently proposed scheme for simulation combining stabiliser decompositions and optimisation strategies implemented in the software QuiZX [Kissinger and van de Wetering, 2022]. With our techniques we manage to reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of minutes on a consumer laptop.
BibTeX - Entry
@InProceedings{kissinger_et_al:LIPIcs.TQC.2022.5,
author = {Kissinger, Aleks and van de Wetering, John and Vilmart, Renaud},
title = {{Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {5:1--5:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16512},
URN = {urn:nbn:de:0030-drops-165128},
doi = {10.4230/LIPIcs.TQC.2022.5},
annote = {Keywords: ZX-calculus, Stabiliser Rank, Quantum Simulation}
}
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Keywords: |
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ZX-calculus, Stabiliser Rank, Quantum Simulation |
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Collection: |
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17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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04.07.2022 |
