R. Alicki, D. A. Lidar, P. Zanardi
Published 2005-06-24, updated 2006-02-10Version 2
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.
Comments: 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
Journal: Phys. Rev. A 73, 052311 (2006)
A sampling-based quasi-probability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise
Geometric phase in open systems: beyond the Markov approximation and weak coupling limit
Exact dynamics of interacting qubits in a thermal environment: Results beyond the weak coupling limit
