Quantum information processing offers potential improvements to a wide range \nof computing endevaors, including cryptography, chemistry simulations and \nmachine learning. The development of practical quantum information processing \ndevices is impeded, however, by challenges arising from the apparent exponential \ndimension of the space one must consider in characterizing quantum \nsystems, verifying their correct operation, and in designing useful control \nsequences. In this work, we address each in turn by providing useful \nalgorithms that can be readily applied in experimental practice. \n \nIn order to characterize the dynamics of quantum systems, we apply statistical \nmethods based on Bayes' rule, thus enabling the use of strong prior \ninformation and parameter reduction. We first discuss an \nanalytically-tractable special case, and then employ a numerical algorithm, \nsequential Monte Carlo, that uses simulation as a resource for characterization. We \ndiscuss several examples of SMC and show its application in nitrogen vacancy \ncenters and neutron interferometry. \nWe then discuss how characterization techniques such as SMC can be used to \nverify quantum systems by using credible region estimation, model selection, \nstate-space modeling and hyperparameterization. Together, these techniques \nallow us to reason about the validity of assumptions used in analyzing quantum \ndevices, and to bound the credible range of quantum dynamics. \n \nNext, we discuss the use of optimal control theory to design robust control \nfor quantum systems. We show extensions to existing OCT algorithms that allow \nfor including models of classical electronics as well as quantum dynamics, \nenabling higher-fidelity control to be designed for cutting-edge experimental \ndevices. Moreover, we show how control can be implemented in parallel across \nnode-based architectures, providing a valuable tool for implementing \nproposed fault-tolerant protocols. \n \nWe close by showing how these algorithms can be augmented using quantum \nsimulation resources to enable addressing characterization and control design \nchallenges in even large quantum devices. In particular, we will introduce a \nnovel genetic algorithm for quantum control design, MOQCA, that utilizes \nquantum coprocessors to design robust control sequences. Importantly, MOQCA is \nalso memetic, in that improvement is performed between genetic steps. We then \nextend sequential Monte Carlo with quantum simulation resources to enable \ncharacterizing and verifying the dynamics of large quantum devices. By using \nnovel insights in epistemic information locality, we are able to learn \ndynamics using strictly smaller simulators, leading to an algorithm we call \nquantum bootstrapping. We demonstrate by using a numerical example of learning \nthe dynamics of a 50-qubit device using an 8-qubit simulator.
Quantum information processing offers potential improvements to a wide range \nof computing endevaors, including cryptography, chemistry simulations and \nmachine learning. The development of practical quantum information processing \ndevices is impeded, however, by challenges arising from the apparent exponential \ndimension of the space one must consider in characterizing quantum \nsystems, verifying their correct operation, and in designing useful control \nsequences. In this work, we address each in turn by providing useful \nalgorithms that can be readily applied in experimental practice. \n \nIn order to characterize the dynamics of quantum systems, we apply statistical \nmethods based on Bayes' rule, thus enabling the use of strong prior \ninformation and parameter reduction. We first discuss an \nanalytically-tractable special case, and then employ a numerical algorithm, \nsequential Monte Carlo, that uses simulation as a resource for characterization. We \ndiscuss several examples of SMC and show its application in nitrogen vacancy \ncenters and neutron interferometry. \nWe then discuss how characterization techniques such as SMC can be used to \nverify quantum systems by using credible region estimation, model selection, \nstate-space modeling and hyperparameterization. Together, these techniques \nallow us to reason about the validity of assumptions used in analyzing quantum \ndevices, and to bound the credible range of quantum dynamics. \n \nNext, we discuss the use of optimal control theory to design robust control \nfor quantum systems. We show extensions to existing OCT algorithms that allow \nfor including models of classical electronics as well as quantum dynamics, \nenabling higher-fidelity control to be designed for cutting-edge experimental \ndevices. Moreover, we show how control can be implemented in parallel across \nnode-based architectures, providing a valuable tool for implementing \nproposed fault-tolerant protocols. \n \nWe close by showing how these algorithms can be augmented using quantum \nsimulation resources to enable addressing characterization and control design \nchallenges in even large quantum devices. In particular, we will introduce a \nnovel genetic algorithm for quantum control design, MOQCA, that utilizes \nquantum coprocessors to design robust control sequences. Importantly, MOQCA is \nalso memetic, in that improvement is performed between genetic steps. We then \nextend sequential Monte Carlo with quantum simulation resources to enable \ncharacterizing and verifying the dynamics of large quantum devices. By using \nnovel insights in epistemic information locality, we are able to learn \ndynamics using strictly smaller simulators, leading to an algorithm we call \nquantum bootstrapping. We demonstrate by using a numerical example of learning \nthe dynamics of a 50-qubit device using an 8-qubit simulator.
For several decades it has been appreciated that quantum computers hold incredible promise to perform calculations intractable to classical computation. However, this promise has be slow to realize. Dozens of quantum systems are currently being investigated for use in quantum information processing - none of which have yet demonstrated algorithms involving more than a handful of qubits and it remains unclear which, if any, of these systems will ultimately compose a scalable, robust quantum information processing architecture. In this thesis we employ analytical, optimal and algebraic control techniques to evaluate various quantum systems for their potential use in quantum information processing. In doing so, we have additionally identified several novel characterization procedures capable of probing both the coherent and incoherent dynamics of quantum systems. The first part of this thesis discusses work motivated by attempts to utilize donor qubits in silicon as quantum bits. We first propose a measurement of the state of a single donor electron spin using two-dimensional electron gas of a field-effect transistor and electrically detected magnetic resonance. We analyze the potential sensitivity of this measurement and show that it is a quantum nondemolition measurement of an electron-encoded state. We then present the first of two novel qubit characterization procedures. We consider the problem of rapidly characterizing a large number of similarly prepared qubits using techniques from optimal experiment design. All qubits are assumed to evolve according to the same physical processes, though the Hamiltonian parameters may vary from device to device - an inevitability in solid state qubits. We use the Cram\\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Though applied to dipole- and exchange-coupled qubits, this technique is widely applicable to other systems. The second part of the thesis discusses the role that control can play in measuring and mitigating noise in qubit systems. Our first result describes a method for quickly simulating the effects of arbitrary markovian noise on qubit systems through the use of a numerically optimized, multi-state Markovian fluctuator. This ability to rapidly simulate the noisy qubit evolution allows us to compute control sequences capable of maximally decoupling the qubit from the noise source. We then introduce the second characterization procedure of the these, showing that a single measurable and controllable qubit may act as a spectrometer of dephasing noise. We show that the formalism of dynamical decoupling can be used to estimate the short-time correlation function of the noise source, while long time correlations may be estimated by a very simple series of free evolution experiments. This technique is applicable to the wide range of physical implementations which suffer from dephasing noise.The final part of this thesis demonstrates that trapped neutral atoms may be utilized for the robust simulation of complex systems exhibiting a topological phase. We present a method to simulate the toric code Hamiltonian stroboscopically, and demonstrate that our technique preserves the ground state degeneracy . Furthermore, we introduce a dissipative mechanism allowing for thermalization of the system to a finite temperature or direct cooling to the ground state manifold.
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.
Recent years have seen quantum computers move from theory to practice, with the first prototypes of \emph{fault-tolerant} quantum computers capable of correcting their own errors. This marks the beginning of an exciting era of \emph{early fault tolerance}, with the first practical applications on the horizon. Among the most promising is quantum simulation, where a quantum computer is used to study another quantum system, such as molecules or materials. However, a central challenge is how to reliably extract accurate information from these early imperfect devices under realistic constraints, including noise, limited qubit numbers, circuit depth, and control. This thesis addresses this challenge by developing and analyzing algorithms for quantum phase estimation in these regimes, a key primitive for determining the energy spectra. It also considers the problem of learning the underlying dynamics of a quantum system, demonstrating the advantage of active control over passive observation. Together, these results contribute to ongoing efforts to overcome the limitations of early quantum hardware through improved algorithms and classical post-processing.
This thesis explores adaptive inference as a tool to characterize quantum systems using experimental data, with applications in sensing, calibration, control, and metrology. I propose and test algorithms for learning Hamiltonian and Kraus operators using Bayesian experimental design and advanced Monte Carlo techniques, including Sequential and Hamiltonian Monte Carlo. Application to the characterization of quantum devices from IBMQ shows a robust performance, surpassing the built-in characterization functions of Qiskit for the same number of measurements. Introductions to Bayesian statistics, experimental design, and numerical integration are provided, as well as an overview of existing literature.
We explore methodologies for characterizing and controlling small quantum systems. We are interested in starting with a description of a quantum system, designing estimators for parameters of the system, developing robust and high-fidelity gates for the system using knowledge of these parameters, and experimentally verifying the performance of these gates. A strong emphasis is placed on using rigorous statistical methods, especially Bayesian ones, to analyze quantum system data. Throughout this thesis, the Nitrogen Vacancy system is used as an experimental testbed. Characterization of system parameters is done using quantum Hamiltonian learning, where we explore the use of adaptive experiment design to speed up learning rates. Gates for the full three-level system are designed with numerical optimal control methods that take into account imperfections of the control hardware. Gate quality is assessed using randomized benchmarking protocols, including standard randomized benchmarking, unitarity benchmarking, and leakage/loss benchmarking.
The potential of quantum computing has captured the interest of the academic and industrial spheres alike. However, the implementation of quantum systems for advantageous computation requires a good deal of further research, much of which must leverage classical computation techniques. In particular, relatively coherent hardware architectures have been fashioned from a variety of quantum systems, and numerous algorithms that are resilient to the noise of near to moderate-term devices have been proposed. In this thesis, we address both of these critical research fronts, exploring the dynamics of optical quantum systems as quantum information platforms and developing variational quantum algorithms. We also discuss the power of efficient tensor network representations for simulating quantum processes. \vspace{0.4cm} First, in the vein of quantum platforms, we develop physical models and operational protocols for both the Nitrogen-vacancy (NV) center in diamond and the dipole-dipole interactions in atomic arrays with subwavelength latice spacing. In the former, we demonstrate that electron-nuclear spin couplings can facilitate all-optical control of the nitrogen nuclear spin, including the manipulation of optical Rabi drives. As decoherent interactions dominate over coherent oscillations, we develop a Bayesian model comparison/parameter fitting framework to affirm the nature of these dynamics. In the later, we analytically characterize the interaction of multiple quantum emitters in a single array, highlighting the potential for long-lived quantum memory and tuneable quantum interactions. \vspace{0.4cm} Then, in the vein of quantum algorithms, we provide a myriad of solutions for the famed ``barren plateau'' problem, as well as introduce two novel algorithms for the circumvention of local minima in nonconvex training landscapes. In the former, we analytically characterize barren plateaus in terms of the spread of entanglement throughout a quantum landscape, framing it in terms of Langevin noise and devising initialization, entanglement regularization, and alternative measurement basis techniques for its curtailment. In the later, 1) Multi-Basis Encoding techniques are devised to improve the performance of quantum optimization algorithms while requiring fewer qubits, as well as highlighting the key features and advantages of tensor-based quantum machine learning simulation, and 2) a Markov chain Monte Carlo protocol for ergodically exploring the quantum optimization landscape (and thus avoiding local minima) is developed.