Breakdown of Surface Code Error Correction Due to Coupling to a Bosonic Bath

Abstract

We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of each quantum error correction period by studying when the single-qubit error rate reaches the corresponding threshold. At the time when error correction breaks down, the error rate in the code can be dominated by the direct coupling of each qubit to the bath, by mediated subluminal interactions, or by mediated superluminal interactions. For a 2D Ohmic bath, the time available per quantum error correction period vanishes in the thermodynamic limit of a large code size $L$ due to induced superluminal interactions, though it does so only like $1/\sqrt{\log L}$. For all other bath types considered, this time remains finite as $L\to \infty$.

16+4 pages, 6 figures

References in corpus (5)

• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Surface Code Threshold in the Presence of Correlated Errors

Cited by in corpus (17)

• Quantum memories at finite temperature
• Multiqubit Spectroscopy of Gaussian Quantum Noise
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Fault-tolerant error correction with the gauge color code
• A repetition code of 15 qubits
• Parallelized quantum error correction with fracton topological codes
• Analysing correlated noise on the surface code using adaptive decoding algorithms
• Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: application to nitrogen vacancy centers
• The dynamical-decoupling-based spatiotemporal noise spectroscopy
• Correcting non-independent and non-identically distributed errors with surface codes
• Dissipative quantum mechanics beyond Bloch-Redfield: A consistent weak-coupling expansion of the ohmic spin boson model at arbitrary bias
• Decoherence of up to 8-qubit entangled states in a 16-qubit superconducting quantum processor
• What determines the ultimate precision of a quantum computer?
• Numerical evaluation of the fidelity error threshold for the surface code
• Revealing correlated noise with single-qubit operations
• Minimising surface-code failures using a color-code decoder
• Symmetry in Multi-Qubit Correlated Noise Errors Enhances Surface Code Thresholds