The Effects of Quantum Error Correction on Noisy Systems
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Date
2018-08-23
Authors
Beale, Stefanie Joyce
Advisor
Laflamme, Raymond
Wallman, Joel
Wallman, Joel
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Full accuracy simulations of quantum systems are very costly, and as a result most studies
of quantum error correction assume a probabilistic Pauli error model, largely because such
errors can be e ciently simulated. Therefore, the behaviour of more general noise in a
quantum error correcting code is poorly characterized. In this thesis, we present results which
demonstrate the scaling of the logical noise with respect to the physical delity, and argue
that the e ective logical noise approaches a Pauli channel as the code distance increases,
even when no recovery operations are applied. As a result, we argue that the average logical
delity can be used to accurately quantify the e ective logical noise, and to select recovery
operations appropriate to the system. We further demonstrate that when physical noise
acts on fewer than d qubits in an [[n; k; d]] code, the resultant noise is Pauli, and develop
a method for approximating the dominant contributions to the e ective logical noise up to
a speci ed precision in terms of the physical in delity. We derive conditions under which
sets of recovery operations will produce equivalent logical noise channels, with examples of
equivalencies in the 3 qubit repetition code, the 5 qubit code, the Steane code, and the Shor
code. We also provide a general expression for the e ective logical noise when the physical
qubits undergo depolarizing or Pauli noise in a quantum error correcting code, examine the
behaviour of depolarizing noise under concatenation of the 5 qubit and Steane codes, and
present an algorithm for soft decoding which is not subject to statistical sampling, with an
emphasis on the e ective behaviour of a concatenated 5 qubit code undergoing depolarizing
noise after applying a specialized version our soft decoding algorithm.
Description
Keywords
Quantum Computing, Quantum Error Correction, Noise, Stabilizer Codes