Avoiding coherent errors with rotated concatenated stabilizer codes

Yingkai Ouyang

doi:10.1038/s41534-021-00429-8

Abstract

Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an [[n, k, d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n, k, d]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code’s potential as a quantum memory.

Highlights

Quantum error correction (QEC) promises to unlock the full potential of quantum technologies by combating the detrimental effects of noise in quantum systems
Prior work either (1) analyzes how existing QEC codes perform under coherent errors without any mitigation of the coherent errors, (2) uses active quantum control which incurs additional resource overheads to mitigate coherent errors offers partial immunity against coherent errors[2] or (3) completely avoids coherent errors using appropriate decoherence-free subspaces (DFS)[3,4,5,6,7,8,9,10,11]
We focus on a family of QEC codes that are compatible with approach (3), and discuss performing QEC protocols with respect to this family of QEC codes

Summary

Introduction

Quantum error correction (QEC) promises to unlock the full potential of quantum technologies by combating the detrimental effects of noise in quantum systems. The ultimate goal in QEC is to protect quantum information under realistic noise models. QEC is most often studied by abstracting away the underlying physics of actual quantum systems, and assumes a simple stochastic Pauli noise model, as opposed to coherent errors which are much more realistic. Pertinent are coherent phase errors that occur on any quantum system that comprises non-interacting qubits with identical energy levels. In such systems, coherent phase errors can result from unwanted collective interactions with stray fields[1], collective drift in the qubits’ energy levels, and fundamental limitations on the precision in estimating the magnitude of the qubits’ energy levels. We focus on a family of QEC codes that are compatible with approach (3), and discuss performing QEC protocols with respect to this family of QEC codes

Methods

Results

Conclusion