A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.

翻译：实现容错量子计算机的关键挑战在于电路优化。针对容错量子计算中最昂贵的门（即T门），我们解决了T计数优化问题，即最小化实现给定电路所需的T门数量。为此，我们开发了AlphaTensor-Quantum——一种基于深度强化学习的方法，该方法利用优化T计数与张量分解之间的关联。与现有T计数优化方法不同，AlphaTensor-Quantum能够整合量子计算领域的专业知识并利用gadgets（辅助结构），从而显著降低优化电路的T计数。在一组算术基准测试中，AlphaTensor-Quantum在T计数优化方面优于现有方法（即使在不使用gadgets的比较中也是如此）。值得注意的是，它发现了一种类似于Karatsuba有限域乘法的高效算法。AlphaTensor-Quantum还为Shor算法和量子化学模拟中使用的相关算术计算找到了最佳人工设计方案，证明其能够以全自动方式优化相关量子电路，节省数百小时的研究时间。