Quantum Error Mitigation in Spin Qubit Systems

Abstract

Quantum computing is commonly expected to have the ability to solve a list of classically infeasible tasks due to the exponentially growth nature of quantum bits (qubits) states in Hilbert space. The physical realization of a fault-tolerant quantum computer requires the error rate of each quantum gate to be lower than a certain threshold. Due to the inevitable interaction between the quantum system and its environment, quantum error mitigation has become a crucial task in quantum computing. Chapter 1 of the thesis introduces some fundamental concepts of spin qubit systems including the double quantum dots (QD), exchange-only (EO) qubits and spin chains and some important previous works about error mitigation in these systems. Chapter 2 delves into the double quantum dot system and establishes a theoretical framework for evaluating the impact of noise on the system based on the filter function. Based on this theoretical framework, the effects of quasi-static noise and non-quasi-static noise are separately extracted as coefficients of each order in certain frequency expansion while the quasi-static noise component can be interpreted as a certain geometric structure, making it more intuitive and easier to optimize. Chapter 3 adopts the approach of constructing more robust logical qubits to perform error mitigation, specifically by treating three spins, which interact only through exchange interactions, as a whole. This allows such a qubit to naturally resist global noise but makes the construction of basic quantum gates challenging, especially in multi-qubit scenarios such as the three-qubit case. Using general theoretical or numerical methods to search for the implementation of a typical quantum gate, such as the Toffoli gate, is extremely challenging. We show that this issue can be addressed efficiently by employing an improved version of Krotov's method, the Jenga-Krotov (JK) algorithm.

Date of Award	8 Sept 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Xin Sunny WANG (Supervisor)