Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective

Abstract

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by QEC using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for long time and/or large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the ``threshold theorem'' of quantum computing is rephrased as a dimensional criterion.

4.1 pages, minor correction and an improved discussion of Eqs. (4) and (14)

References in corpus (7)

• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• A Theory of Quantum Error-Correcting Codes
• Fault-tolerant quantum computation with long-range correlated noise
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Decoherence by Correlated Noise and Quantum Error Correction

Cited by in corpus (23)

• Spin-Based Quantum Computers made by Chemistry: Hows and Whys
• Fault-tolerant quantum computation versus Gaussian noise
• Distance Bounds on Quantum Dynamics
• Errors and pseudo-thresholds for incoherent and coherent noise
• Surface Code Threshold in the Presence of Correlated Errors
• Hamiltonian Formulation of Quantum Error Correction and Correlated Noise: The Effects Of Syndrome Extraction in the Long Time Limit
• Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models
• Decoherence in quantum walks and quantum computers
• Experimental quantification of spatial correlations in quantum dynamics
• Radiation Eigenmodes of Dicke Superradiance
• Fidelity of the surface code in the presence of a bosonic bath
• Superradiance as a Source of Collective Decoherence in Quantum Computers
• Quantum Metrology in Correlated Environments
• Bound on quantum computation time: Quantum error correction in a critical environment
• Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise
• Effect of quantum error correction on detection-induced coherent errors
• Quantum Error Correction Code in the Hamiltonian Formulation
• Surface code fidelity at finite temperatures
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space
• Long-time efficacy of the surface code in the presence of a superohmic environment
• Sufficient condition on noise correlations for scalable quantum computing
• Large Sample Superradiance and Fault-Tolerant Quantum Computation
• Quantum Error Correction of Time-Correlated Errors