Bound on quantum computation time: Quantum error correction in a critical environment

Abstract

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user.

4 pages (revised title, following PRA request)

References in corpus (8)

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Cited by in corpus (7)

• Surface Code Threshold in the Presence of Correlated Errors
• Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models
• Fidelity of the surface code in the presence of a bosonic bath
• Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise
• Surface code fidelity at finite temperatures
• Long-time efficacy of the surface code in the presence of a superohmic environment
• Sufficient condition on noise correlations for scalable quantum computing