Randomised benchmarking with gate-dependent noise : plus applications in the triple quantum dot qubit

• Main Author: Zaw, Lin Htoo
• Other Authors: Koh Teck Seng
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2020
• Subjects: Science::Physics::Atomic physics::Quantum theory; Science::Mathematics::Applied mathematics::Information theory
• Online Access: https://hdl.handle.net/10356/140343
• Institution: Nanyang Technological University

Quantum computers promise a major speedup over their classical counterparts by taking advantage of quantum effects. However, this increased performance is hindered by the tendency of quantum computers to be considerably error-prone. Therefore, the identification and elimination of noise processes in quantum systems are needed before general purpose quantum computers can be practically useful. The study of noise characterisation methods is an important part of this effort towards fault tolerant computation. This thesis presents the theoretical derivation and some numerical results of randomised benchmarking, a scalable noise characterisation method that estimates the average error rate of a set of quantum gates. Existing treatments of randomised benchmarking are often steeped heavily with mathematical details of representation theory, which can be inaccessible to many readers. Instead, the analytical portion of this paper is built up using concepts that can be found in any standard quantum information text. In particular, the superoperator-density operator formalism is explicitly constructed from the familiar description of pure states and quantum processes with the Dirac notation, and the twirl of a quantum channel is found using its effect on an arbitrary density operator without any allusion to the standard method of utilising Schur's lemma. In the latter part of this paper, randomised benchmarking is used to study the triple quantum dot qubit, which is a likely candidate for fault-tolerant computation. Using numerical simulations, the triple quantum dot qubit was found to be robust against detuning noise, but is particularly sensitive towards tunnelling noise. The type of dominant noise was also found to affect the sweet spot behaviour of the qubit. Finally some preliminary work towards a better optimised operation of the triple quantum dot qubit and more sophisticated noise characterisation methods are also presented.