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.

arXiv comment16 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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Cited by in corpus (22)

• Nonstabilizerness determining the hardness of direct fidelity estimation
• Cutting multi-control quantum gates with ZX calculus
• Stabilizer Tensor Networks with Magic State Injection
• Quantum circuit compilation and hybrid computation using Pauli-based computation
• Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus
• Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences
• The Basis of Design Tools for Quantum Computing: Arrays, Decision Diagrams, Tensor Networks, and ZX-Calculus
• Abstraqt: Analysis of Quantum Circuits via Abstract Stabilizer Simulation
• Completeness of the ZH-calculus
• Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions
• Picturing Counting Reductions with the ZH-Calculus
• Lower T-count with faster algorithms
• Procedurally Optimised ZX-Diagram Cutting for Efficient T-Decomposition in Classical Simulation
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
• Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning
• A recursively partitioned approach to architecture-aware ZX Polynomial synthesis and optimization
• Fast Classical Simulation of Quantum Circuits via Parametric Rewriting in the ZX-Calculus
• ViCAR: Visualizing Categories with Automated Rewriting in Coq
• Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach
• String Diagrams for Defect-Based Surface Code Computing
• Polynomial-Time Classical Simulation of Hidden Shift Circuits via Confluent Rewriting of Symbolic Sums
• A Graphical #SAT Algorithm for Formulae with Small Clause Density