近日，日本东京大学Yamasaki, Hayata团队报道了具有多对数时间和恒定空间开销的容错量子计算。该研究于2025年11月26日发表在《自然—物理学》杂志上。

容错量子计算面临的核心挑战在于同时降低空间开销（即每个逻辑量子比特所需的大量物理量子比特）和时间开销（即实现逻辑门所需的冗长物理门序列）。

研究组证明，结合非零码率量子低密度奇偶校验码（QLDPC）与级联Steane码的协议，可实现恒定的空间开销和多项式对数级的时间开销，即使计入必要的经典处理过程。该协议在现有恒定空间开销协议基础上实现了性能提升。为证明此结论，研究组开发了名为"部分电路约简"的技术，通过分析由少量模块构成的子电路，即可完成对整个容错电路的错误分析。

借助此方法，研究组修正了现有QLDPC码恒定空间开销协议在阈值定理证明中存在的逻辑漏洞，补全了其理论证明。该研究证实，基于QLDPC码的方案能够以可忽略的时间延迟和物理量子比特的有界开销，实现容错量子计算。

附：英文原文

Title: Fault-tolerant quantum computation with polylogarithmic time and constant space overheads

Author: Tamiya, Shiro, Koashi, Masato, Yamasaki, Hayata

Issue&Volume: 2025-11-26

Abstract: A major challenge in fault-tolerant quantum computation is to reduce both the space overhead, that is, the large number of physical qubits per logical qubit, and the time overhead, that is, the long physical gate sequences needed to implement a logical gate. Here we prove that a protocol using non-vanishing-rate quantum low-density parity-check (QLDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for the required classical processing. This protocol offers an improvement over existing constant-space-overhead protocols. To prove our result, we develop a technique that we call partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets. With this approach, we resolve a logical gap in the existing arguments for the threshold theorem for the constant-space-overhead protocol with QLDPC codes and complete its proof. Our work establishes that the QLDPC-code-based approach can realize fault-tolerant quantum computation with a negligibly small slowdown and a bounded overhead of physical qubits. Quantum low-density parity-check codes are anticipated to be an efficient approach to quantum error correction. Now it has been proven that these codes can be time-efficient with only a constant overhead in the required number of qubits.

DOI: 10.1038/s41567-025-03102-5

Source: https://www.nature.com/articles/s41567-025-03102-5