Near-term quantum computers are expected to work in an environment where each operation is noisy, with no error correction. Therefore, quantum-circuit optimizers are applied to minimize the number of noisy operations. Today, physicists are constantly experimenting with novel devices and architectures. For every new physical substrate and for every modification of a quantum computer, we need to modify or rewrite major pieces of the optimizer to run successful experiments. In this paper, we present QUESO, an efficient approach for automatically synthesizing a quantum-circuit optimizer for a given quantum device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with high-probability correctness guarantees for IBM computers that significantly outperforms leading compilers, such as IBM's Qiskit and TKET, on the majority (85%) of the circuits in a diverse benchmark suite. A number of theoretical and algorithmic insights underlie QUESO: (1) An algebraic approach for representing rewrite rules and their semantics. This facilitates reasoning about complex symbolic rewrite rules that are beyond the scope of existing techniques. (2) A fast approach for probabilistically verifying equivalence of quantum circuits by reducing the problem to a special form of polynomial identity testing. (3) A novel probabilistic data structure, called a polynomial identity filter (PIF), for efficiently synthesizing rewrite rules. (4) A beam-search-based algorithm that efficiently applies the synthesized symbolic rewrite rules to optimize quantum circuits.

翻译：近期量子计算机预计将在无纠错、每步操作均存在噪声的环境中运行。因此，量子电路优化器被用于最小化噪声操作的数量。当前，物理学家们持续尝试新型器件与架构。每当出现新的物理基底或量子计算机的修改版本时，我们都需修改或重写优化器主要模块以成功开展实验。本文提出QUESO——一种为给定量子器件自动合成量子电路优化器的高效方法。例如，在1.2分钟内，QUESO可为IBM计算机合成具有高概率正确性保障的优化器，其性能在多样化基准测试套件中的大多数电路（85%）上显著超越主流编译器（如IBM Qiskit与TKET）。QUESO的理论与算法基础包括：（1）一种用于表示重写规则及其语义的代数方法，实现了对超越现有技术范畴的复杂符号重写规则的推理；（2）一种通过将问题归约为多项式恒等式检测的特殊形式，实现量子电路等价性概率验证的快速方法；（3）一种名为多项式恒等过滤器（PIF）的新型概率数据结构，用于高效合成重写规则；（4）一种基于束搜索的算法，可高效应用所合成的符号重写规则优化量子电路。