Almost Linear Decoder for Optimal Geometrically Local Quantum Codes

Quinten Eggerickx

Adam Wills

Ting-Chun Lin

Kristiaan De Greve

Min-Hsiu Hsieh

出版日期

June 23, 2025

研究中心

量子計算研究所

主題

Quantum Computing

內容目錄

Geometrically local quantum codes, which are error-correction codes embedded in ℝ𝐷 with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to achieve geometrically local codes that maximize both the dimension and the distance, as well as the energy barrier of the code. In this work, we focus on the constructions involving subdivision, and we show that they have an almost linear time decoder, obtained by combining the decoder of the outer good qLDPC code and a generalized version of the Union-Find decoder. This provides the first decoder for an optimal geometrically local three-dimensional code. We demonstrate the existence of a finite threshold error rate under the code capacity noise model using a minimum weight perfect matching decoder. Furthermore, we argue that this threshold is also applicable to the decoder based on the generalized Union-Find algorithm.