Exhaustive Search for Quantum Circuit Optimization using ZX Calculus

2025-03-14

AI Summary

Circuit optimization under constrained quantum hardware resources remains challenging, particularly when preserving strict semantic equivalence without relying on application-specific metrics. Method: This paper introduces the first exhaustive search optimization framework for quantum circuits based on the ZX-calculus. It formally defines the exhaustive optimization problem over ZX-diagrams and integrates depth-first search with iterative deepening to optimize objectives such as T-count and edge count. A novel set of pruning rules is designed to ensure convergence and solution quality despite the non-terminating nature of the underlying rewrite system. Contribution/Results: Evaluated on 100 standard benchmark circuits, the method achieves significant reductions in both T-count and circuit depth. The framework has been integrated into PyZX and Qiskit as a production-ready compiler optimization pass, enabling deployment within mainstream quantum software stacks.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a restricted number of available physical qubits and quantum gates, short coherence time, and high error rates. This paper lays the foundation towards a metric independent approach to quantum circuit optimization based on exhaustive search algorithms. This work uses depth-first search and iterative deepening depth-first search. We rely on ZX calculus to represent and optimize quantum circuits through the minimization of a given metric (e.g. the T-gate and edge count). ZX calculus formally guarantees that the semantics of the original circuit is preserved. As ZX calculus is a non-terminating rewriting system, we utilise a novel set of pruning rules to ensure termination while still obtaining high-quality solutions. We provide the first formalization of quantum circuit optimization using ZX calculus and exhaustive search. We extensively benchmark our approach on 100 standard quantum circuits. Finally, our implementation is integrated in the well-known libraries PyZX and Qiskit as a compiler pass to ensure applicability of our results.

Problem

• Optimizes quantum circuits using ZX calculus and exhaustive search.
• Ensures circuit semantics preservation through ZX calculus rules.
• Integrates optimization into PyZX and Qiskit for practical application.

Innovation

• Exhaustive search for quantum circuit optimization
• ZX calculus for circuit representation and optimization
• Novel pruning rules ensure termination and quality