Avoiding coherent errors with rotated concatenated stabilizer codes

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.

8 pages, 5 figures, two columns

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• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
• Logarithmic-Depth Quantum Circuits for Hamming Weight Projections
• Effect of quantum error correction on detection-induced coherent errors
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space
• High-Rate Amplitude-Damping Shor Codes with Immunity to Collective Coherent Errors
• Robust projective measurements through measuring code-inspired observables
• Error Crafting in Mixed Quantum Gate Synthesis
• Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
• Quantum dual extended Hamming code immune to collective coherent errors