Almost Linear Decoder for Optimal Geometrically Local Quantum Codes
arXiv:2411.02928 · doi:10.1103/sxdx-qbcz
Abstract
Geometrically local quantum codes, which are error correction codes embedded in 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 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.
19 pages, 9 figures. We corrected the noise model from circuit-level to code-capacity. An incorrect threshold proof was removed; we now prove a threshold for MWPM and argue applicability to our decoder. We added motivation and discuss applicability to codes in arXiv:2303.06755 and arXiv:2309.16503. Typos have been fixed
References in corpus (12)
- Quantum Error Correction for Quantum Memories
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- 3D integrated superconducting qubits
- Tradeoffs for reliable quantum information storage in 2D systems
- Solid-state qubits integrated with superconducting through-silicon vias
- Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
- Parallel window decoding enables scalable fault tolerant quantum computation
- Parallelized quantum error correction with fracton topological codes
- Proof of finite surface code threshold for matching
- Coherent spin qubit shuttling through germanium quantum dots
- Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device
- Single-shot decoding of good quantum LDPC codes