Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes

TL;DR

This paper introduces a new fault-tolerant quantum computation scheme that significantly reduces time overhead for qLDPC codes, enabling faster and more resource-efficient quantum computing.

Contribution

The authors develop a scheme that achieves constant qubit overhead and minimized time overhead, outperforming previous methods for a broad class of qLDPC codes.

Findings

Achieves $O(d^{1+o(1)})$ time overhead for good qLDPC codes.

Provides techniques for parallelized code surgery with constant qubit overhead.

Establishes a new paradigm for accelerating fault-tolerant quantum computation.

Abstract

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$ qLDPC code with constant encoding rate and distance $d = \Omega(n^{1/a})$. For good qLDPC codes, the time overhead is minimized and reaches $O(d^{1+o(1)})$. In contrast, code surgery based on gauging measurement and brute-force branching requires a time overhead of $O(dw^{1+o(1)})$, where $d\leq w\leq n$. Thus, our scheme is asymptotically faster for all codes with $a < 2$. This speedup is achieved by developing techniques that enable parallelized code surgery under constant qubit overhead and leverage classical locally testable codes for efficient resource state preparation. These results establish a new paradigm for accelerating fault-tolerant quantum computation on qLDPC codes, while maintaining low overhead and broad applicability.