AI 中文总结
该研究证明量子容错无法实现恒定时空开销，仅可实现恒定相对开销，给出达到存储器界的CSS码构造及相关电路规模界，确立量子容错资源的基本限制。
AI 中文摘要
阈值定理指出，量子计算可在物理错误阈值以下实现可靠运行，代价是额外的物理量子比特和电路深度。近期研究已将这些空间和时间开销降低至多对数或近对数标度，但累积时空开销能否为恒定值仍不清楚。本文中，我们证明即使是量子存储器中最简单的量子信息保存任务，在乐观噪声模型下且允许通用自适应协议，累积时空开销也存在不可避免的对数贡献。不过，这一额外成本可在多个逻辑量子比特间分摊，因此足够宽的计算（包括Shor算法的标准实现）仍可能实现恒定相对开销。我们进一步给出达到该存储器界的正码率CSS码构造，确定相同标度从量子存储器扩展到容错电路实现的充分条件，并推导子系统时空码的电路规模界。我们的工作确立了量子容错所需资源的基本限制。
英文摘要
The threshold theorem states that quantum computations can be made reliable below a physical error threshold, at the cost of additional physical qubits and circuit depth. Recent work has reduced these space and time overheads to polylogarithmic or nearly logarithmic scalings, but whether the cumulative spacetime overhead can be constant has remained unclear. Here, we show that even for the simplest task of preserving quantum information in a quantum memory, under an optimistic noise model and allowing general adaptive protocols, there is an unavoidable logarithmic contribution to the cumulative spacetime overhead. This additional cost can nevertheless be shared among many logical qubits, so sufficiently wide computations, including standard implementations of Shor's algorithm, may still achieve constant relative overhead. We further give a positive-rate CSS code construction that attains the memory bound, identify sufficient conditions under which the same scaling extends from quantum memory to fault-tolerant circuit implementations, and derive circuit-size bounds for subsystem spacetime codes. Our work establishes fundamental limits on the resources required for quantum fault tolerance.
Comments40 pages
