Message passing in fault tolerant quantum error correction

Abstract

Inspired by Knill's scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical information obtained at the first level is used to help interpret the syndrome at the second level, our scheme will correct all cases with four physical errors. This results in a reduction of the logical failure rate relative to conventional error correction by a factor proportional to the reciprocal of the physical error rate.

8 pages, 9 figures

References in corpus (11)

• Fault-tolerant quantum computation by anyons
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Simulated Quantum Computation of Molecular Energies
• Quantum Computing with Very Noisy Devices
• Fault-tolerant quantum computation with high threshold in two dimensions
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Overhead and noise threshold of fault-tolerant quantum error correction
• Active stabilisation, quantum computation and quantum state synthesis
• Subsystem fault tolerance with the Bacon-Shor code
• Effective fault-tolerant quantum computation with slow measurements
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes

Cited by in corpus (5)

• A logical qubit in a linear array of semiconductor quantum dots
• Accuracy threshold for concatenated error detection in one dimension
• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Optimal correction of concatenated fault-tolerant quantum codes
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited