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.

量子电路中 T 门计数的最小化是实现容错量子计算的关键挑战之一，本文提出了一种基于深度强化学习的方法 AlphaTensor-Quantum，利用张量分解与 T 门优化之间的关系，通过引入量子计算的领域专业知识和利用 gadgets，显著降低了优化电路的 T 门计数，从而在算术基准测试中超越了现有的 T 门计数优化方法，同时还发现了一种类似于 Karatsuba 算法的高效乘法算法，并成功优化了 Shor 算法中的相关算术计算和量子化学模拟，实现了在完全自动化的方式下，优化相关量子电路，节省了数百小时的研究时间。