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Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions
Authors
Aleks Kissinger 
,
John van de Wetering ,
Renaud Vilmart
-
Part of:
Volume:
17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2022-07-04
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Document Identifiers
Author Details
- Radboud University Nijmegen, The Netherlands
- University of Oxford, United Kingdom
Acknowledgements
JvdW and AK would like to thank James Hefford for useful discussions regarding decompositions of cat states in the ZX-calculus.
Cite As Get BibTex
Aleks Kissinger, John van de Wetering, and Renaud Vilmart. Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.TQC.2022.5
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Quantum computation theory
Keywords
- ZX-calculus
- Stabiliser Rank
- Quantum Simulation
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