Rescaling decoder for two-dimensional topological quantum color codes on 4.8.8 lattices

Physical Review A, vol. 106

Abstract

Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes, are leading candidates for practical scalable quantum error correction and require efficient and scalable decoders. In this work, we propose and study the efficiency of a decoder for two-dimensional topological color codes on the 4.8.8 lattice (also known as the square-octagon code), by building on the work of Sarvepalli and Raussendorf [Phys. Rev. A 85, 022317 (2012)], for color codes on hexagonal lattices. The decoder is based on a rescaling approach, in which syndrome information on a part of the qubit lattice is processed locally, and then the lattice is rescaled iteratively to smaller sizes. We find a threshold of 6.0% for code capacity noise.

Authors 3

1. Pedro Parrado-Rodríguez

   Swansea University

   Affiliation as printed

   Department of Physics, College of Science, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom

2. Manuel Rispler Aachen Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany

3. Markus Michael Müller Aachen Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany