Quantum Weight Reduction with Layer Codes

TL;DR

This paper introduces a simple quantum weight reduction method that lowers check weight and qubit degree by replacing code elements with surface code patches, forming Layer Codes suitable for modular architectures.

Contribution

A novel, straightforward quantum weight reduction procedure that achieves lower check weight and qubit degree using surface code patches, improving upon existing methods.

Findings

Achieves check weight 6 and qubit degree 6.

Replaces each code element with surface code patches.

Suitable for modular quantum architectures.

Abstract

Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this work we introduce a simple and general procedure for quantum weight reduction that achieves check weight 6 and total qubit degree 6, lower than existing procedures at the cost of a potentially larger qubit overhead. Our quantum weight reduction procedure replaces each qubit and check in an arbitrary Calderbank-Shor-Steane code with an ample patch of surface code, these patches are then joined together to form a geometrically nonlocal Layer Code. This is a quantum analog of the simple classical weight reduction procedure where each bit and check is replaced by a repetition code. Due to the simplicity of our weight reduction procedure, bounds on the weight and degree of the resulting code follow directly from the Layer Code construction and hence are easily verified by inspection. Our procedure is well suited for implementation in modular architectures that consist of surface code patches networked via long-range interconnects.