Decoherence by Correlated Noise and Quantum Error Correction

Abstract

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.

4 pages, 1 figure, Phys. Rev. Lett. in press

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• Hamiltonian Formulation of Quantum Error Correction and Correlated Noise: The Effects Of Syndrome Extraction in the Long Time Limit
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• Log-domain decoding of quantum LDPC codes over binary finite fields
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• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
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• Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise
• Surface code fidelity at finite temperatures
• Decoherence in quantum cavities: Environmental erasure of carpet-type structures
• Impurity-Induced Environmental Quantum Phase Transitions in the Quadratic-Coupling Spin-Boson Model
• Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model At Finite Temperature
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• Quantum Error Correction of Time-Correlated Errors
• Relaxation times do not capture logical qubit dynamics