Vanishing 2-Qubit Gates with Non-Simplification ZX-Rules

TL;DR

This paper introduces a novel quantum circuit optimization method using non-simplification ZX-rules and heuristic algorithms to significantly reduce 2-qubit gates, outperforming existing techniques on various benchmarks.

Contribution

It presents a new approach leveraging local congruences in ZX-diagrams combined with heuristic search to optimize quantum circuits beyond traditional methods.

Findings

Reduces 2-qubit gates by up to 46% on benchmark circuits

Outperforms state-of-the-art optimization techniques in 87% of cases

Achieves an additional 15-30% circuit complexity reduction

Abstract

Traditional quantum circuit optimization is performed directly at the circuit level. Alternatively, a quantum circuit can be translated to a ZX-diagram which can be simplified using the rules of the ZX-calculus, after which a simplified circuit can be extracted. However, the best-known extraction procedures can drastically increase the number of 2-qubit gates. In this work, we take advantage of the fact that local changes in a ZX-diagram can drastically affect the complexity of the extracted circuit. We use a pair of congruences (i.e., non-simplification rewrite rules) based on the graph-theoretic notions of local complementation and pivoting to generate local variants of a simplified ZX-diagram. We explore the space of equivalent ZX-diagrams generated by these congruences using simulated annealing and genetic algorithms to obtain a simplified circuit with fewer 2-qubit gates. On randomly generated circuits, our method can outperform state-of-the-art optimization techniques for low-qubit (<10) circuits. On a set of previously reported benchmark circuits with <=14 qubits, our method outperforms off-the-shelf methods in 87% of cases, consistently reducing overall circuit complexity by an additional ~15-30% and eliminating up to 46% of 2-qubit gates. These preliminary results serve as a proof-of-concept for a new circuit optimization strategy in the ZX-calculus.