Almost-linear time decoding algorithm for topological codes

Author:

Delfosse Nicolas123,Nickerson Naomi H.4

Affiliation:

1. IQIM, California Institute of Technology, Pasadena, CA, USA

2. Department of Physics and Astronomy, University of California, Riverside, CA, USA

3. Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA

4. Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

Abstract

In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(nα(n)), where n is the number of physical qubits and α is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, α(n)3. We prove that our algorithm performs optimally for errors of weight up to (d1)/2 and for loss of up to d1 qubits, where d is the minimum distance of the code. Numerically, we obtain a threshold of 9.9% for the 2d-toric code with perfect syndrome measurements and 2.6% with faulty measurements.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Cited by 67 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Efficient percolation simulations for lossy photonic fusion networks;Physical Review Research;2024-09-10

2. Fast erasure decoder for hypergraph product codes;Quantum;2024-08-27

3. Long-range-enhanced surface codes;Physical Review A;2024-08-08

4. Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits;Quantum;2024-08-02

5. Quantum Network Routing Based on Surface Code Error Correction;2024 IEEE 44th International Conference on Distributed Computing Systems (ICDCS);2024-07-23

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3