紧凑且具表达力的量子电路优化方法的合成
Synthesis of Compact and Expressive Quantum-Circuit Optimizations
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中文总结 AI 辅助
针对噪声量子设备的电路优化问题，提出带形式化保证的QSymb框架，合成紧凑且具表达力的量子电路重写规则，在两类门集的基准测试中均优于现有优化器，实现显著的两量子比特门减少。
中文摘要 AI 辅助
当前量子设备存在噪声问题，因此减小电路规模对可靠执行至关重要。现有的基于规则的优化器通常依赖庞大的规则集，难以管理且仍会遗漏长距离变换。我们提出QSymb，一个用于合成紧凑且具表达力的量子电路重写规则并带有形式化保证的框架。我们将符号重写规则形式化，其中符号门代表无限多个子电路。随后我们定义形式为$L;S = S;R$的规范符号规则，并证明它们构成一个紧凑的生成核心，可从中推导出通用符号规则。在该形式化基础上，给定门集，QSymb合成：(1)一个小型、不可推导的具体规则集，在选定的规模和量子比特边界下是完备的；(2)一个小型但具表达力的规范符号规则集，可捕获超出有限或仅单项式模式的变换。我们进一步提出规则锚定，用于从规范符号规则中推导优化有效的规则。这些结果共同提供了表达力和保证：通过验证、不可推导性和有界完备性确保合成规则的正确性。在IBM-Eagle门集上，QSymb在90%、67%、82%、85%和83%的标准量子算法基准测试中，分别在两量子比特门减少方面严格优于最先进的基于重写的优化器Qiskit、Guoq、Quartz、TKET和Queso；在Nam门集上，相应比例为88%、74%、81%、86%和82.9%。它分别实现了27.44%和29.95%的最终平均两量子比特门减少。
英文摘要
Today's quantum devices are noisy, so reducing circuit size is critical for reliable execution. Existing rule-based optimizers often rely on large rule sets that are difficult to manage and still miss long-distance transformations. We present QSymb, a framework for synthesizing compact and expressive quantum-circuit rewrite rules with formal guarantees. We formalize symbolic rewrite rules in which a symbolic gate represents infinitely many subcircuits. We then define canonical symbolic rules of the form $L;S = S;R$ and prove that they constitute a compact generative core from which general symbolic rules can be derived. On top of this formal foundation, given a gate set, QSymb synthesizes (1) a small, non-derivable concrete rule set that is complete up to chosen size and qubit bounds, and (2) a small but expressive canonical symbolic rule set that captures transformations beyond finite or monomial-only patterns. We further present rule anchoring to derive optimization-effective rules from canonical symbolic rules. Together, these results provide both expressiveness and guarantees: soundness of synthesized rules via validation, non-derivability, and bounded completeness. On the IBM-Eagle gate set, QSymb strictly outperforms state-of-the-art rewrite-based optimizers (Qiskit, Guoq, Quartz, TKET, and Queso) in two-qubit-gate reduction on 90%, 67%, 82%, 85%, and 83% of standard quantum algorithm benchmarks, respectively; on Nam gate set, the corresponding rates are 88%, 74%, 81%, 86%, and 82.9%. It achieves final average two-qubit-gate reductions of 27.44% and 29.95%, respectively.
发表机构
- Columbia University（哥伦比亚大学）
- CertiK
机构由 AI 辅助整理，请以论文原文为准。
