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：近期的量子计算机预计将在无纠错、每个操作都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。目前，物理学家不断实验新型器件和架构。对于每一种新的物理衬底以及量子计算机的每一次修改，都需要修改或重写优化器的主要组件以成功运行实验。本文提出QUESO，一种针对给定量子器件自动综合量子电路优化器的高效方法。例如，在1.2分钟内，QUESO能够为IBM计算机综合出具有高概率正确性保证的优化器，该优化器在多样化基准测试套件中的大多数（85%）电路上显著优于主流编译器（如IBM的Qiskit和TKET）。QUESO背后的理论和算法创新包括：（1）一种代数方法用于表示重写规则及其语义，这有助于推理超出现有技术范围的复杂符号重写规则；（2）一种通过将问题归约为特殊形式的多项式恒等式测试来概率性验证量子电路等价性的快速方法；（3）一种称为多项式恒等式过滤器（PIF）的新型概率数据结构，用于高效综合重写规则；（4）一种基于束搜索的算法，可高效应用综合得到的符号重写规则来优化量子电路。