用强化学习优化量子线路中的T门和CS门数量,显著提升合成效率。
Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning
- 基于通道表示与整数矩阵运算,设计高效强化学习框架。
- 实现最多100个T门的两量子比特线路,比前人提升5倍。
- 在不增加辅助量子比特情况下,降低关键算子的门数43%以上。
本文研究强化学习(RL)在量子电路合成中的应用,目标是优化可通过Clifford+T和Clifford+CS门集精确实现的酉算子的T-count和CS-count。我们设计的RL框架采用酉算子的通道表示,支持仅用整数进行高效矩阵运算,并引入剪枝启发式与算子规范化的策略以降低搜索复杂度。相比已有方法,本方法能在更短时间内合成更大规模的酉算子,成功率与改进幅度均显著提升。在两量子比特的Clifford+T合成中,成功实现最多100个T门的接近最优分解,是此前RL算法的5倍,也是当前所有方法中最大实例。该算法还复现了已知的一量子比特最优线性复杂度T-count合成算法。对于重要基元如受控循环移位(减少43%)、受控加法器(减少14.3%)和乘法器(减少14%),在不添加额外辅助量子比特的情况下实现了显著的渐近门数缩减。对于两量子比特的Clifford+CS单元,算法达到线性复杂度,此前仅有基于SO(6)表示的方法可实现此目标。
原文摘要 · Abstract (English)
In this paper we study the potential of using reinforcement learning (RL) in order to synthesize quantum circuits, while optimizing the T-count and CS-count, of unitaries that are exactly implementable by the Clifford+T and Clifford+CS gate sets, respectively. We have designed our RL framework to work with channel representation of unitaries, that enables us to perform matrix operations efficiently, using integers only. We have also incorporated pruning heuristics and a canonicalization of operators, in order to reduce the search complexity. As a result, compared to previous works, we are able to implement significantly larger unitaries, in less time, with much better success rate and improvement factor. Our results for Clifford+T synthesis on two qubit unitaries achieve close-to-optimal decompositions for up to 100 T gates, 5 times more than previous RL algorithms and to the best of our knowledge, the largest instances achieved with any method to date. Our RL algorithm is able to recover previously-known optimal linear complexity algorithm for T-count-optimal decomposition of 1 qubit unitaries. We illustrate significant reduction in the asymptotic T-count estimate of important primitives like controlled cyclic shift (43%), controlled adder (14.3%) and multiplier (14%), without adding any extra ancilla. For 2-qubit Clifford+CS unitaries, our algorithm achieves a linear complexity, something that could only be accomplished by a previous algorithm using SO(6) representation.
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