Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions

TL;DR

This paper presents an advanced classical simulation method for quantum circuits that combines stabiliser decompositions with ZX-calculus simplifications, significantly reducing computational complexity for large circuits.

Contribution

It introduces a novel approach integrating ZX-calculus with stabiliser decompositions for more efficient quantum circuit simulation.

Findings

Able to simulate 50- and 100-qubit circuits with up to 70 T-gates

Achieved stabiliser decompositions many orders smaller than previous methods

Performed exact norm calculations on circuits with over 1000 T-gates

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.