Causal flow preserving optimisation of quantum circuits in the ZX-calculus

Holker, Calum · 2023

| 编号 NA118 | 主题 线路综合与等价验证 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

2023 · 预印本；未核实后续正式发表 Optimising quantum circuits to minimise resource usage is crucial, especially with near-term hardware limited by quantum volume. This paper introduces an optimisation algorithm aiming to minimise non-Clifford gate count and two-qubit gate count by building on ZX-calculus-based strategies. By translating a circuit into a ZX-diagram it can be simplified before being extracted back into a circuit. We assert that simplifications preserve a graph-theoretic property called causal flow. This has the advantage that qubit lines are well defined throughout, permitting a trivial extraction procedure and in turn enabling the calculation of an individual transformation’s impact on the resulting circuit. A general procedure for a decision strategy is introduced, inspired by an existing heuristic based method. Both phase teleportation and the neighbour unfusion rule are generalised. In particular, allowing unfusion of multiple neighbours is shown to lead to significant improvements in optimisation. When run on a set of benchmark circuits, the algorithm developed reduces the two-qubit gate count by an average of 19.8%, beating both the previous best ZX-based strategy (14.6%) and non-ZX strategy (18.5%) at the time of publication. This lays a foundation for multiple avenues of improvement. A particularly effective strategy for optimising QFT circuits is also noted, resulting in exactly one two-qubit gate per non-Clifford gate.

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