Addressable gate-based logical computation with quantum LDPC codes

TL;DR

This paper presents a novel gate-based protocol enabling addressable logical operations on individual qubits encoded with quantum LDPC codes, reducing overhead and enhancing scalability for fault-tolerant quantum computing.

Contribution

It introduces a new scheme for performing logical Clifford gates on quantum LDPC codes using auxiliary Bacon-Shor codes and teleportation, allowing fully addressable, gate-based quantum computation.

Findings

Demonstrates implementation of an overcomplete logical Clifford gate set

Shows numerical evaluation of error-correction performance

Integrates with magic state protocols for universal quantum computing

Abstract

Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet realizing high-rate fault-tolerant computation with these codes remains a central challenge. Apart of the lattice surgery approach, standard schemes for realizing logical gates have so far been restricted to performing global operations on all logical qubits at the same time. Another approach relies on low-rate code switching methods. In this work, we introduce a gate-based protocol for addressable single- and multi-qubit Clifford operations on individual logical qubits encoded within one or more quantum LDPC codes. Our scheme leverages logical transversal operations via an auxiliary Bacon-Shor code to perform logical operations with constant time overhead enabled by teleportation. We demonstrate the implementation of an overcomplete logical Clifford gate set and perform numerical simulations to evaluate the error-correction performance of our protocol. Finally, we observe that our scheme can be integrated with magic state cultivation protocols to achieve universal, gate-based, and fully addressable quantum computation.