A term-rewriting system for computer quantum algebra

Knuth-Bendix Completion Algorithm and Shuffle Algebras For Compiling NISQ Circuits

Compiling quantum circuits lends itself to an elegant formulation in the language of rewriting systems on non commutative polynomial algebras $\mathbb Q\langle X\rangle$. The alphabet $X$ is the set of the allowed hardware 2-qubit gates. The set of gates that we wish to implement from $X$ are elements of a free monoid $X^*$ (obtained by concatenating the letters of $X$). In this setting, compiling an idealized gate is equivalent to computing its unique normal form with respect to the rewriting system $\mathcal R\subset \mathbb Q\langle X\rangle$ that encodes the hardware constraints and capabi…

Validating quantum computers using randomized model circuits

We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values as high as 16. The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system. It quantifies the largest random circuit of equal width and depth that the computer successfully implements. Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and c…

ZX-DB：基于ZX-演算的量子电路化简与重写图数据库

ZX-DB: A Graph Database for Quantum Circuit Simplification and Rewriting via the ZX-Calculus

针对量子电路编译优化需求，本文提出基于ZX-演算的图数据库系统ZX-DB，将重写规则编码为openCypher查询在Memgraph上执行，相较PyZX最高实现一个数量级的独立重写加速，开辟了数据库支撑量子计算流水线的新方向。

通过ZX-微积分中的参数化重写实现量子电路的快速经典模拟

Fast Classical Simulation of Quantum Circuits via Parametric Rewriting in the ZX-Calculus

针对ZX-微积分结合Clifford求和技术模拟量子电路时重复计算问题，提出参数化约简图的策略，通过GPU并行加速最终阶段，在特定任务中较非参数化方法平均提速78.3±10.2倍。

已认证的雾态重写（问答指南）

Certified Misty-State Rewriting (A Question-and-Answer Guide)

该研究提出雾态语言这一直观量子力学教育符号，可让学生提前理解量子电路，其是连接教育符号与数学明确语义的特定场景桥梁，不替代ZX等完整图形演算。

Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing

This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. [...] The first major contribution of this dissertation is the introduction of a…