Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions

Abstract

We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum circuits can be classically simulated by expressing the non-stabiliser gates in a circuit as magic state injections and decomposing them in chunks of 2-6 states at a time, obtaining sums of (efficiently-simulable) stabiliser states with many fewer terms than the naive approach. We adapt these techniques from the original setting of Clifford circuits with magic state injection to generic ZX-diagrams and show that, by interleaving this "chunked" decomposition with a ZX-calculus-based simplification strategy, we can obtain stabiliser decompositions that are many orders of magnitude smaller than existing approaches. We illustrate this technique to perform exact norm calculations (and hence strong simulation) on the outputs of random 50- and 100-qubit Clifford+T circuits with up to 70 T-gates as well as a family of hidden shift circuits previously considered by Bravyi and Gosset with over 1000 T-gates.

16 pages, 6 charts, and many figures. For instructions on running associated software, see https://github.com/Quantomatic/quizx/blob/stabrank-v1/stabrank.md

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• Abstraqt: Analysis of Quantum Circuits via Abstract Stabilizer Simulation
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• Procedurally Optimised ZX-Diagram Cutting for Efficient T-Decomposition in Classical Simulation
• A recursively partitioned approach to architecture-aware ZX Polynomial synthesis and optimization
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• String Diagrams for Defect-Based Surface Code Computing
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• A Graphical #SAT Algorithm for Formulae with Small Clause Density
• Polynomial-Time Classical Simulation of Hidden Shift Circuits via Confluent Rewriting of Symbolic Sums