Classical simulation of quantum circuits with partial and graphical stabiliser decompositions

TL;DR

This paper introduces improved classical simulation techniques for quantum circuits using partial and graphical stabiliser decompositions, leveraging ZX-calculus to efficiently simulate larger circuits with fewer stabiliser terms.

Contribution

It presents a novel method employing ZX-calculus and partial stabiliser decompositions to speed up quantum circuit simulation, applicable to circuits of any size.

Findings

Achieved simulation of 50-qubit, 1400 T-count circuits in minutes.

Developed a technique requiring 2^{0.396 t} stabiliser terms for T-count t.

Matched previous asymptotic scaling results with a method applicable to any circuit size.

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 $2^{\alpha t}$ stabiliser terms, where $\alpha\approx 0.396$, to simulate a circuit with T-count $t$. This matches the $\alpha$ found by Qassim et al., 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. 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.