Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit

Abstract

We critically examine the internal consistency of a set of minimal assumptions entering the theory of fault-tolerant quantum error correction for Markovian noise. These assumptions are: fast gates, a constant supply of fresh and cold ancillas, and a Markovian bath. We point out that these assumptions may not be mutually consistent in light of rigorous formulations of the Markovian approximation. Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction). The former is incompatible with the assumption of a constant and fresh supply of cold ancillas, while the latter is inconsistent with fast gates. We discuss ways to resolve these inconsistencies. As part of our discussion we derive, in the weak coupling limit, a new master equation for a system subject to periodic driving.

19 pages. v2: Significantly expanded version. New title. Includes a debate section in response to comments on the previous version, many of which appeared here http://dabacon.org/pontiff/?p=959 and here http://dabacon.org/pontiff/?p=1028. Contains a new derivation of the Markovian master equation with periodic driving

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Cited by in corpus (9)

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• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Hamiltonian Formulation of Quantum Error Correction and Correlated Noise: The Effects Of Syndrome Extraction in the Long Time Limit
• Precision characterisation of two-qubit Hamiltonians via entanglement mapping
• Quantum nondemolition-like, fast measurement scheme for a superconducting qubit
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Phase-space theory for dispersive detectors of superconducting qubits
• Approximate quantum error correction for correlated noise