Density Matrix Simulation of Quantum Error Correction
(2020) PHYM01 20201Atomic Physics
Department of Physics
- Abstract
- Quantum error correction will be integral in developing full scale quantum computers, but as of yet beneficial quantum error correction has not been demonstrated experimentally. An important question is therefore what prerequisites need to be met to achieve this. Results of density matrix simulations of the performance of the seven qubit Steane code in a quantum computing setting are presented. The full density matrix was kept throughout the whole simulations, which means that all errors can be accounted for. In particular, the importance of the circuit depth, i.e. the number of gates in series before error correction is applied, for the overall performance was investigated. It was found that the depth of the circuit has a large impact on... (More)
- Quantum error correction will be integral in developing full scale quantum computers, but as of yet beneficial quantum error correction has not been demonstrated experimentally. An important question is therefore what prerequisites need to be met to achieve this. Results of density matrix simulations of the performance of the seven qubit Steane code in a quantum computing setting are presented. The full density matrix was kept throughout the whole simulations, which means that all errors can be accounted for. In particular, the importance of the circuit depth, i.e. the number of gates in series before error correction is applied, for the overall performance was investigated. It was found that the depth of the circuit has a large impact on the threshold error rate for which error correction becomes beneficial. A gain parameter was defined, which describes the largest constant factor by which errors can be suppressed. It was shown that there is a trade-off between the threshold error and the gain; The highest threshold value was found to be around p_th~10^-4, which is in line with other estimates, but the maximum gain for this value was only 3. To achieve a gain of 100, an error rate of p_err~2x10^-9 is required. In addition, performance statistics such as run-time as a function of circuit depth and width for the matlab code used for simulations are presented. (Less)
- Popular Abstract
- A major obstacle when trying to construct a quantum computer is that the components of the computer are extremely sensitive to noise from various sources. One way to protect against this noise is by using a so-called error correcting code. This thesis investigates the performance of a particular error correcting code, called the Steane code.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9029902
- author
- Rolander, Arvid LU
- supervisor
- organization
- course
- PHYM01 20201
- year
- 2020
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- quantum error Correction, density matrix simulation, Steane code
- language
- English
- id
- 9029902
- date added to LUP
- 2020-09-29 16:59:13
- date last changed
- 2020-09-29 16:59:13
@misc{9029902,
abstract = {{Quantum error correction will be integral in developing full scale quantum computers, but as of yet beneficial quantum error correction has not been demonstrated experimentally. An important question is therefore what prerequisites need to be met to achieve this. Results of density matrix simulations of the performance of the seven qubit Steane code in a quantum computing setting are presented. The full density matrix was kept throughout the whole simulations, which means that all errors can be accounted for. In particular, the importance of the circuit depth, i.e. the number of gates in series before error correction is applied, for the overall performance was investigated. It was found that the depth of the circuit has a large impact on the threshold error rate for which error correction becomes beneficial. A gain parameter was defined, which describes the largest constant factor by which errors can be suppressed. It was shown that there is a trade-off between the threshold error and the gain; The highest threshold value was found to be around p_th~10^-4, which is in line with other estimates, but the maximum gain for this value was only 3. To achieve a gain of 100, an error rate of p_err~2x10^-9 is required. In addition, performance statistics such as run-time as a function of circuit depth and width for the matlab code used for simulations are presented.}},
author = {{Rolander, Arvid}},
language = {{eng}},
note = {{Student Paper}},
title = {{Density Matrix Simulation of Quantum Error Correction}},
year = {{2020}},
}