对抗性错误下的容错量子计算
Fault-Tolerant Quantum Computation with Adversarial Errors
- University of Bristol（布里斯托大学）
- UC Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究证明了对抗性全局最坏情况非马尔可夫噪声下的容错量子计算可行性，提出基于子系统乘积码的方案，解决了量子PCP构造的关键瓶颈。
AI中文摘要：
我们证明了对抗噪声下量子计算的容错定理。对于深度为$\bar{T}$、包含$\bar{N}$个逻辑量子位的任意量子电路，我们构造了一个由$N=\text{poly}(\bar{N})$个物理量子位构成的容错电路，其深度为$\bar{T}\times\bar{N}^{o(1)}$，该电路可抵御在每个时间步骤中任意选择并破坏近乎线性数量$N^{1-o(1)}$个物理量子位的对手。这种鲁棒性显著优于此前的容错定理，后者假设破坏要么是局部且随机的，要么仅作用于量子位的多项式级消失分数。我们的容错方案解决了通过Anshu、Breuckmann和Nguyen（STOC'24）的电路到哈密顿映射构造量子PCP的关键瓶颈。更根本地，我们的结果表明，在全局、最坏情况且计算全程非马尔可夫的噪声模型下，容错量子计算仍然可行，直接反驳了关联噪声可能从根本上破坏量子容错的担忧。我们的构造基于新的子系统乘积码族，这类码具有大维度、大距离和低重量奇偶校验，且支持横向非Clifford门。我们展示了如何基于经典张量码的局部可检验性，使用类Floquet过程对这些码执行单次容错纠错。随后，我们通过在超立方量子位架构中重复码切换，获得通用容错方案。最后，我们递归地将自身方案与自身组合，以将初始指数级量子位维度降至常数。
英文摘要：
We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on $\bar{N}$ logical qudits of depth $\bar{T}$, we construct a fault-tolerant circuit on $N=\text{poly}(\bar{N})$ physical qudits of depth $\bar{T}\cdot\bar{N}^{o(1)}$, which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number $N^{1-o(1)}$ of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.
