We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and pivoting and show that the resulting reduced diagram can be transformed back into a quantum circuit. While little is known about extracting circuits from arbitrary ZX-diagrams, we show that the underlying graph of our simplified ZX-diagram always has a graph-theoretic property called generalised flow, which in turn yields a deterministic circuit extraction procedure. For Clifford circuits, this extraction procedure yields a new normal form that is both asymptotically optimal in size and gives a new, smaller upper bound on gate depth for nearest-neighbour architectures. For Clifford+T and more general circuits, our technique enables us to to `see around' gates that obstruct the Clifford structure and produce smaller circuits than naive 'cut-and-resynthesise' methods.
An Exactness Barrier for ZX-Calculus Optimization of Synthesized Clifford+T Circuits
University Paris City（巴黎城市大学）；University of Reunion（留尼汪大学）；Dipartimento di Fisica e Chimica Emilio Segrè, Università degli Studi di Palermo（巴勒莫大学埃米利奥·塞格雷物理与化学系）；Department of Mathematics, University of Colombo（科伦坡大学数学系）；School of Physics, Mathematics and Computing, University of Western Australia（西澳大利亚大学物理、数学与计算学院）；PEACCEL, AI for Biologics（PEACCEL生物制剂人工智能公司）
Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications
Institute for Theoretical Physics（理论物理研究所）；Center for Complex Systems Studies（复杂系统研究中心）；Utrecht University（乌得勒支大学）；Utrecht Institute of Linguistics OTS（乌得勒支语言学研究所OTS）
A Quantum-Control Lambda-Calculus with Multiple Measurement Bases
Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Universidad Nacional de Quilmes（基尔梅斯国立大学）；Universidad Argentina de la Empresa（阿根廷企业大学）；Universidad de la República（共和国大学）
