Quantum Optimal Control via Error-Resilient Gate Compilation

Abstract

Achieving high-fidelity quantum control in the presence of experimental noise is a fundamental requirement for scalable quantum computing. This thesis combines optimal control and gate compilation to develop a series of error-resilient gate compilation strategies that enable robust implementation of both single- and two-qubit gates, focusing on practical approaches that enhance gate fidelity. By combining analytical insights with numerical optimization, the presented methods address key challenges in quantum gate calibration and error mitigation, offering solutions that are compatible with a wide range of quantum hardware platforms.

For single-qubit operations, we introduce an error-resilient gate compilation framework that decomposes arbitrary gates into sequences of single-qubit rotations through a fixed angle around the x-axis—referred to as rotation X gates—with individually optimized phase shifts. This approach circumvents the need for complex pulse shaping or extended waveform durations, greatly simplifying experimental calibration. Crucially, the method leverages the universality of control phases and requires only the calibration of a single X gate, making it highly adaptable to different physical qubit implementations. Numerical simulations in spin qubit systems demonstrate substantial suppression of errors arising from frequency fluctuations and microwave crosstalk, establishing a scalable route to high-fidelity single-qubit control.

For two-qubit gates, with an emphasis on the controlled-rotation and CNOT gates, we propose an analytical compilation protocol that utilizes four microwave pulses with tunable phases. This scheme significantly reduces calibration overhead by relying only on the calibration of a single cross-resonance gate with a fixed duration. Furthermore, we develop an error-resilient gate compilation protocol for the CNOT gate, wherein the operation is partitioned into four segments with numerically optimized control phases. Simulations reveal that this strategy markedly enhances the robustness and fidelity of two-qubit gates, even in the presence of realistic noise and crosstalk, thereby paving the way for scalable entangling operations in semiconductor spin qubits.

In summary, this thesis presents experimentally feasible and theoretically grounded compilation techniques for error-resilient quantum control. The proposed frameworks for both single- and two-qubit gates offer significant advantages in terms of noise robustness, calibration efficiency, and hardware compatibility. These advances contribute to the ongoing effort to realize practical, high-fidelity quantum computing across diverse quantum platforms.

Date of Award	11 Sept 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Xin Sunny WANG (Supervisor)