Dynamic T-decomposition for classical simulation of quantum circuits

TL;DR

The paper tackles the classical simulation of quantum circuits by extending stabilizer (T-)decompositions through dynamic, structure-aware vertex cuts within ZX-calculus. It introduces a family of dynamic T-decompositions that exploit common ZX-patterns to achieve favorable effective efficiencies $α_{\text{eff}}$ after ZX simplification, outperforming prior universal methods on several circuit classes. A greedy-cut heuristic selects between decompositions to maximize simplification, and empirical benchmarks on CCZ, IQP, modified hidden shift, and Pauli-exponential circuits show significant runtime reductions for most classes. The approach broadens the toolkit for classical simulation, enabling larger circuits to be simulated efficiently and offering concrete decompositions with scalable, pattern-driven applicability.

Abstract

It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{αt})$ time, given $t$ non-Clifford gates and a decomposition efficiency $α$. The past years have seen a number of papers presenting new decompositions of lower $α$ to reduce this runtime and enable simulation of ever larger circuits. More recently, it has been demonstrated that well placed applications of apparently weaker (higher $α$) decompositions can in fact result in better overall efficiency when paired with the circuit simplification strategies of ZX-calculus. In this work, we take the most generalized T-decomposition (namely vertex cutting), which achieves a poor efficiency of $α=1$, and identify common structures to which applying this can, after simplification via ZX-calculus rewriting, yield very strong effective efficiencies $α_{\text{eff}}\ll1$. By taking into account this broader scope of the ZX-diagram and incorporating the simplification facilitated by the well-motivated cuts, we derive a handful of efficient T-decompositions whose applicabilities are relatively frequent. In benchmarking these new 'dynamic' decompositions against the existing alternatives, we observe a significant reduction in overall $α$ and hence overall runtime for classical simulation, particularly for certain common circuit classes.

Figures (9)

• Figure 1: The basic components of a ZX-diagram, namely Z- and X-spiders, as well as Hadamard edges (being a yellow box or a blue dashed edge) and normal edges.
• Figure 2: The basic rewriting rules weteringWorking of ZX-calculus, where $a\in\{0,1\}$ and $\alpha,\beta\in[0,2\pi)$. These rules remain valid with all colors inverted.
• Figure 3: A ZX-diagram in reduced gadget form Kissinger-2022.
• Figure 4: The measured results for classically simulating CCZ circuits, versus the method of Kissinger et al. Kissinger2022cat
• Figure 5: The measured results for classically simulating modified hidden shift circuits, versus the method of Kissinger et al. Kissinger2022cat

Theorems & Definitions (2)

• Definition 1: IQP circuit Bremner-2016codsi2023
• Definition 2: $\beta$ efficiency