Scalable Constant-Time Logical Gates for Large-Scale Quantum Computation Using Window-Based Correlated Decoding

TL;DR

This paper introduces a scalable architecture for fault-tolerant quantum computing that achieves constant-time logical gates using window-based correlated decoding, reducing overhead and supporting large-scale quantum algorithms.

Contribution

It proposes a novel architecture combining delayed fixup circuits with window-based correlated decoding for scalable, constant-time logical gates in large-scale quantum computation.

Findings

Supports universal logical gates across various quantum codes.

Reduces decoding frequency and duration significantly.

Demonstrates potential with Shor's algorithm on ion trap systems.

Abstract

Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed correlated decoding and ``algorithmic fault tolerance" to achieve constant-time logical gates that enables universal quantum computation. However, for circuits involving mid-circuit measurements and feedback, the previous scheme for constant-time logical gates is incompatible with window-based decoding, which is a scalable approach for handling large-scale circuits. In this work, we propose an architecture that employs delayed fixup circuits and window-based correlated decoding, realizing scalable constant-time logical gates. This design significantly reduces both the frequency and duration of decoding, while maintaining support for constant-time and universal logical gates across a broad class of quantum codes. More importantly, by spatial parallelism of windows, this architecture well adapts to time-optimal FTQC, making it particularly useful for large-scale quantum computation. Using Shor's algorithm as an example, we explore the application of our architecture and reveals the promising potential of using constant-time logical gates to perform large-scale quantum computation with acceptable overhead on physical systems like ion traps.