THE EFFECT OF THE ANCILLA VERIFICATION ON THE QUANTUM ERROR CORRECTION

<p>Communication is the prototypical application of error-correction methods. To communicate, a sender needs to convey information to a receiver over a noisy "communication channel." Such a channel can be thought of as a means of transmitting an information-carrying physical system from one place to another. During transmission, the physical system is subject to disturbances (noise) that can adversely affect the information carried. To use a communication channel, the sender needs to encode the information to be transmitted in the physical system. After transmission, the receiver decodes the information. Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal with both noise on stored quantum information, and also with faulty quantum gates, faulty quantum preparation,and faulty measurements. In this dissertation, we look at how additional information about the structure of the quantum circuit and noise can improve or alter the performance of techniques in quantum error correction. Chapter 1 and 2, are an introduction to the quantum computation, quantum error correction codes and fault-tolerant quantum computing. These chapters are written to be a useful for students at the graduate and advanced undergraduate level. Also. The first two chapters of this dissertation will be useful to researchers in other fields who would like to understand how quantum error correction and fault-tolerant quantum computing are possible. In chapter 3, we present numerical simulation results comparing the logical error rates for the fault-tolerant [[7, 1, 3]] 's 7 code using the technique of ancilla verification vs. the newer method of ancilla decoding as described in [1]. In chapter 4, we determine how often one should apply error correction. Therefore, we provide a relationship between the logical error rate and the physical error rate for a sequence of logical gates, sometimes followed by noisy quantum error correction</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date.available

2015

Author dc:creator

• Abu-Nada, Ali

Contributors dc:contributor

• Byrd, Mark

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/1037

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-2041