Title: A Review on Quantum Circuit Optimization using ZX-Calculus Show Chinese title

Title: 基于ZX-演算的量子电路优化综述

Abstract: Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit depth). Quantum circuit optimization is a key mitigation strategy. In this context, ZX-calculus has emerged as an alternative framework that allows for semantics-preserving quantum circuit optimization. We review ZX-based optimization of quantum circuits, categorizing them by optimization techniques, target metrics and intended quantum computing architecture. In addition, we outline critical challenges and future research directions, such as multi-objective optimization, scalable algorithms, and enhanced circuit extraction methods. This survey is valuable for researchers in both combinatorial optimization and quantum computing. For researchers in combinatorial optimization, we provide the background to understand a new challenging combinatorial problem: ZX-based quantum circuit optimization. For researchers in quantum computing, we classify and explain existing circuit optimization techniques. Show Chinese abstract

Abstract: 量子计算对于某些算法有望实现显著的速度提升，但当前噪声中等规模量子（NISQ）时代计算机的实际应用仍受限于资源约束（例如，噪声、量子位、门和电路深度）。量子电路优化是一种关键的缓解策略。在此背景下，ZX演算作为一种替代框架出现，允许进行语义保持的量子电路优化。我们回顾了基于ZX的量子电路优化，根据优化技术、目标指标和预期的量子计算架构对其进行分类。此外，我们概述了关键挑战和未来研究方向，如多目标优化、可扩展算法和增强的电路提取方法。这项综述对组合优化和量子计算领域的研究人员都有价值。对于组合优化领域的研究人员，我们提供了理解一个新的具有挑战性的组合问题：基于ZX的量子电路优化的背景。对于量子计算领域的研究人员，我们对现有的电路优化技术进行了分类和解释。