Fault-tolerant quantum computation cannot be achieved with constant spacetime overhead

2026-08-26

AI Summary

研究证明了即使在乐观噪声模型下，量子信息存储也存在不可避免的对数级时空开销，并探讨了实现容错量子计算所需资源的基本限制。

Abstract

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.

Problem

• fault-tolerant quantum computation
• spacetime overhead
• quantum memory
• error threshold
• qubits

Innovation

• logarithmic spacetime overhead
• quantum fault tolerance
• CSS code construction