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Quantum Control Protocols for Robust Quantum Computing

Leeseok Kim

Published May 16, 2026• 0 citations
OpenAlex

Abstract

The fundamental goal of quantum computing is to precisely control quantum systems to perform meaningful tasks, including implementing high-fidelity quantum gates for reliable quantum computation and accurately simulating complex quantum many- body dynamics. In this dissertation, we develop improved quantum control protocols for three distinct objectives, quantum error suppression, quantum optimal control, and analog quantum algorithms, achieving performance beyond standard approaches. First, we introduce new dynamical decoupling protocols, including both determin- istic and randomized constructions, that can substantially outperform conventional deterministic sequences. We then extend the randomized approach to dynamically corrected gates. Second, we propose a randomized quantum optimal control frame- work that offers advantages over deterministic optimal control protocols. Finally, we develop new control protocols for analog quantum algorithms to perform high-order Hamiltonian simulation and learning unknown quantum states.

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The fundamental goal of quantum computing is to precisely control quantum systems to perform meaningful tasks, including implementing high-fidelity quantum gates for reliable quantum computation and accurately simulating complex quantum many- body dynamics. In this dissertation, we develop improved quantum control protocols for three distinct objectives, quantum error suppression, quantum optimal control, and analog quantum algorithms, achieving performance beyond standard approaches. First, we introduce new dynamical decoupling protocols, including both determin- istic and randomized constructions, that can substantially outperform conventional deterministic sequences. We then extend the randomized approach to dynamically corrected gates. Second, we propose a randomized quantum optimal control frame- work that offers advantages over deterministic optimal control protocols. Finally, we develop new control protocols for analog quantum algorithms to perform high-order Hamiltonian simulation and learning unknown quantum states.
This study optimizes qubit control protocols using optimal control theory, machine learning, and stochastic modeling to enhance quantum computing performance. Quantum computing represents a transformative leap in computational power, with qubits serving as the fundamental building blocks of quantum information processing. However, the efficient control and manipulation of qubits remain significant challenges due to decoherence, noise, and imperfect control pulses. This study focuses on optimizing qubit control protocols using advanced applied mathematical techniques, including optimal control theory, machine learning, and stochastic modeling, to enhance quantum computing performance. By leveraging these techniques, we develop robust control strategies that minimize errors, improve gate fidelity, and extend coherence times. Our methodology integrates numerical simulations with experimental validation, demonstrating significant improvements in qubit control accuracy and reliability. The results highlight the potential of these optimized protocols to enable scalable and fault-tolerant quantum computing. This work contributes to the ongoing efforts to realize practical quantum technologies, offering insights into the interplay between mathematical optimization and quantum system dynamics.
Quantum computing and quantum information science are two recently discovered and rapidly growing fields of physics that show substantial promise in providing new and valuable technologies in the foreseeable future. Large-scale quantum computers, if ever realized experimentally, are likely to outperform their classical counterparts in a number of important computational tasks, the most important of which may be the accurate simulation of many-body quantum systems such as the ones encountered in physics, chemistry and life sciences. This thesis investigates the problem of controlling quantum systems for the purpose of performing quantum information processing tasks. The problem is approached from a theoretical and simulational viewpoint. The work contained here encompasses a range of levels of abstraction. Firstly, we discuss the decomposition of abstract multiqubit logic gates into sequences of simple elementary gates. Secondly, we study the local commutational properties of two-qubit gates using local gate invariants. Thirdly, we develop methods for the physical implementation of the elementary gates through the control of specific quantum systems, possibly in the presence of noise and decoherence. We present a new, almost optimal n-qubit gate decomposition based on the cosine-sine decomposition, which utilizes a likewise new intermediate quantum circuit structure we call a uniformly controlled gate. We then show how they can be used in constructing a general state transformation circuit. Both of the resulting circuits can be efficiently implemented using nearest-neighbor gates which makes their physical realization simpler. A local gate invariant is introduced which can be used to assess the suitability of two-qubit gates for serving as the entangling gate in elementary gate libraries. Finally, we develop numerical optimization methods for finding near-optimal control sequences for generating oneand two-qubit gates, both in closed quantum systems and in the presence of Markovian noise.
Abstract : This project aimed to address the most significant challenge facing the development of large-scale quantum computers: suppressing hardware error. Through this work we focused on the realization of a robust, high-fidelity Quantum Control Toolkit that is fully transportable between different quantum computing technology platforms. The techniques encapsulated herein were designed to provide qubit robustness to decoherence during memory (dynamical decoupling DD), and increase the fidelity of qubit operations undertaken in the presence of random environmental noise and control imperfections (dynamically corrected gates DCGs, and composite pulses CPs). This project has seen the demonstration of significant hardware-based improvements in quantum control fidelity along with the full experimental validation of an engineering-inspired filter-transfer function framework for quantum control.
Constructing high-fidelity control pulses that are robust to control and system/environment fluctuations is a crucial objective for quantum information processing (QIP). We combine dynamical decoupling (DD) with optimal control (OC) to identify control pulses that achieve this objective numerically. Previous DD work has shown that general errors up to (but not including) third order can be removed from {pi}- and {pi}/2-pulses without concatenation. By systematically integrating DD and OC, we are able to increase pulse fidelity beyond this limit. Our hybrid method of quantum control incorporates a newly-developed algorithm for robust OC, providing a nested DD-OC approach to generate robust controls. Motivated by solid-state QIP, we also incorporate relevant experimental constraints into this DD-OC formalism. To demonstrate the advantage of our approach, the resulting quantum controls are compared to previous DD results in open and uncertain model systems.
This thesis details work performed on the improvement of experimental control of quantum systems through the use of optimal control theory. We pursue this objective through both conceptual and practical routes. We first devise improved methods of optimal control for quantum systems. We then apply them, as well as more established methods, to experimental situations where robustness to inaccuracy and error is sought. We develop a method for improving the computational efficiency of optimal control theory in the context of quantum control. This approach makes use of the iterative nature of optimisation algorithms, by using perturbation theory to minimise the effort needed to calculate the time propagator associated with a controlled Hamiltonian. We also create a new way of defining a figure of merit when optimising for robustness against error in an experiment. This method specifically applies to errors that have a relatively small effect on the controlled system's Hamiltonian. We compare this with an ensemble method based around randomly sampling several points on the control landscape, and find these methods to be largely equivalent for small errors, with the ensemble method being superior for larger error. On the applied side, we design radio frequency magnetic pulses that create robustness in spin ensembles to inhomogeneous broadening and variations of coupling strength to the control field for two applications. In the first, we create reliable gates in a situation where limitations are imposed on the control that can be applied. In the second application, we design controls for radio frequency magnetic pulses to create a superradiant state in a spin ensemble. Finally, we collaborate with the experiment to measure the electrons electric dipole moment that is being performed at Imperial College London. For this collaboration, we shape the envelope of the radio frequency control pulses used in the experiment to create superpositions of Zeeman and Stark-shifted excited states in YbF molecules. This shaping allows us to impart pre-determined phases to these superpositions, in a manner that is robust to errors in the control pulse envelope. We obtain sets of robust and sensitive pulses that have been sent to the experiment for testing purposes.
We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed.