Practical applications of machine learning to quantum computing and quantum simulation
Advisor
Gong, ZhexuanDate issued
2022Keywords
autoregressive artificial neural network variational groundstate searchmachine learning
matrix product operator supervised quantum state tomography
nonlinear unsupervised learning
quantum manybody physics
quantum optimal control  pulse optimization for fast 2qubit gates
Metadata
Show full item recordAbstract
The understanding of quantum manybody systems is at the core of various quantum technologies that could revolutionize our society, including quantum computing and quantum simulation in particular. This thesis focuses on practical applications of machine learning to the simulation, control, and understanding of quantum manybody systems. First, variational learning using artificial neural networks is leveraged to achieve efficient classical simulation of quantum manybody systems and is further developed to allow GPU accelerated computing. Second, a machine learning based quantum optimal control algorithm is developed to design speedoptimized quantum gates for a superconducting qubit based quantum computer. Its advantage over conventional algorithms is demonstrated both theoretically and experimentally. Third, unsupervised machine learning is applied to identify complex quantum phase transitions. A specific method known as diffusion map is shown to be capable of learning a wide range of nontrivial quantum phases and is applicable to stateofart quantum simulation experiments. Finally, a new quantum state tomography protocol based on supervised machine learning is developed, which outperforms many existing protocols especially for states generated by onedimensional noisy quantum computers. Each of these achievements is integral to the development of quantum technologies in realistic settings.Rights
Copyright of the original work is retained by the author.Collections
Related items
Showing items related by title, author, creator and subject.

Quantum complexity: quantum mutual information, complex networks, and emergent phenomena in quantum cellular automataCarr, Lincoln D.; Vargas, David L.; Behn, Cecilia D.; Kohl, Patrick B. (Patrick Brian); Toberer, Eric (Colorado School of Mines. Arthur Lakes Library, 2016)Emerging quantum simulator technologies provide a new challenge to quantum many body theory. Quantifying the emergent order in and predicting the dynamics of such complex quantum systems requires a new approach. We develop such an approach based on complex network analysis of quantum mutual information. First, we establish the usefulness of quantum mutual information complex networks by reproducing the phase diagrams of transverse Ising and BoseHubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to nonequilibrium quantum dynamics. We conclude with a study of student collaboration networks, correlating a student's role in a collaboration network with their grades. This work thus initiates a quantitative theory of quantum complexity and provides a new tool for physics education research. We find that network density, clustering coefficient, disparity, and Pearson R correlation show systematic finite size scaling towards critical points of the transverse Ising model and the BoseHubbard model. Using matrix product state methods we are able to simulate lattices of hundreds of qubits, allowing us to verify the critical point of the transverse Ising model to within 0.001% of its known value. Furthermore, we find that complex network analysis identifies the BerezinskiiKosterlitzThouless critical point of the BoseHubbard to within 3.6% of its accepted value. Finally, we identify the boundary separating the Mott Insulator phase from a superfluid phase in the BoseHubbard model by extremizing network density, clustering coefficient, and disparity. After studying the static properties of quantum many body systems, we study the entanglement and complexity generated by Hamiltonian based quantum cellular automata. In quantum cellular automata one defines a set of local rules that govern the evolution of the quantum state. A site in a quantum lattice evolves if the set of sites around it are in certain configurations. Configurations are defined in terms of the number of sites in the ``alive'' state about a site. We quantify entanglement in terms of the central bond entropy, and complexity in terms of persistent fluctuations of the central bond entropy, complex network measures of quantum mutual information networks far from their values for random/well known quantum states, and robust dynamical features. These Hamiltonians are a generalization of the Bleh, Calarco, Montangero Hamiltonian. Before beginning our study of the entanglement and complexity generated by these Hamiltonians we first perform a convergence analysis of the dynamics of the Bleh, Calarco, Montangero Hamiltonian using an open source matrix product state code, Open Source Matrix Product States. We find that the Bleh, Calarco, Montangero Hamiltonian rapidly saturates the entanglement cutoff of Open Source Matrix Product States for all initial conditions studied and is thus not a viable numerical method for studying the dynamics of quantum cellular automata. We conclude our convergence study with a case study of an emergent quantum blinker pattern also observed in exact simulation and a case study of a nearest neighbor quantum cellular automata. We conclude that while for generic initial conditions Open Source Matrix Product States is unable to meet its internal convergence criteria, for particular initial conditions and quantum cellular automata it is able to provide reliable estimates of entanglement and complexity measures. The failure of OpenMPS to provide reliably converged quantum states leads us to study our quantum cellular automata using a Trotterbased time evolution scheme. We quantify the entanglement and complexity generated by 13 nextnearest neighbor quantum cellular automata. We also define Goldilocks rules, rules that produce activity at a site if there are exactly the right number of alive sites in the neighborhood of a site, not too few, not too many. We identify a Goldilocks rule, rule 4, as the best complexitygenerating rule out of the 13 rules tested, verifying our hypothesis that only Goldilocks rules are complexity generating. We also find that nonGoldilocks rules tend toward thermalization as quantified by reduced fluctuations in the central bond entropy. We find that both highly entangled quantum states and lowly entangled quantum states have complex structure in their quantum mutual information adjacency matrices. Finally, in keeping with the strong physics education research focus at the Colorado School of Mines, we apply complex network analysis to a key issue germane to the student experience, namely student collaboration networks. We compute nodal centrality measures on the collaboration networks of students enrolled in three upperdivision physics courses at the Colorado School of Mines. These are networks in which links between students indicate assistance with homework. The courses included in the study are intermediate classical mechanics, introductory quantum mechanics, and intermediate electromagnetism. We find that almost all of the measures considered correlate with analytical homework grades. In contrast only net outstrength correlates with exam grade. The benefits of collaboration do not extend from homework to exams, and students who help more than they are helped perform well on exams. Centrality measures between simultaneous collaboration networks (analytical vs. numerical homework collaboration) composed of the same students correlate with each other. Students take on similar roles in response to analytical vs. numerical homework assignments. Changes in collaboration across semesters are also considered as students transition from classical mechanics in the fall to quantum mechanics and electromagnetism in the spring. We find the most frequent transition is that students that help many others and have high grades will continue to help many others and have high grades. Students that help few more frequently transition from low grades to high grades than students that help many.

Quantum confinement in silicon clathrate quantum dotsLusk, Mark T.; Brawand, Nicholas P.; Lusk, Mark T.; Toberer, Eric; Wood, David M. (Colorado School of Mines. Arthur Lakes Library, 2013)The relationship between crystal structure and quantum confinement is quantified by computationally analyzing sets of silicon quantum dots associated with nine types of clathrates. Density functional theory is used to show that bulk energy gap between the highest occupied and lowest unoccupied KohnSham orbitals varies by more than 1 eV, both above and below that of diamond silicon. The approach is also used to relate dot size to energy gap to identify a linear correlation between quantum confinement sensitivity and bulkcrystal effective mass. All clathrates are found to have a confinement sensitivity less than that of diamond silicon. Bulk properties (gap and effective mass) can therefore be used to identify clathrate semiconductors with promising optoelectronic properties. For example, the combined gap and confinement sensitivity of Type VII clathrate results in a low energy gap for quantum dots within 1 to 2 nm in diameter, making type VII worthy of consideration for efficient multiple exciton generation and other optoelectronic applications.

Macroscopic quantum tunneling and quantum manybody dynamics in BoseEinstein condensatesCarr, Lincoln D.; Wu, Mingzhong; Alcala, Diego A.; Tenorio, Luis; Pankavich, Stephen; Flammer, P. David (Colorado School of Mines. Arthur Lakes Library, 2020)Quantum mechanics revolutionized the previous century, not only in technology with lasers and semiconductors but also our fundamental view of the world with Bell's inequality and entanglement. Quantum tunneling was the first experimental verification of quantum mechanics, by solving the mystery of radioactive decay, that a particle can escape the nucleus without sufficient energy to overcome the classical energy barrier. In this century, manybody quantum mechanics is bringing about a second revolution, with the possibility of quantum simulators, quantum computers, and a deeper understanding the nature. However, in order to fully harness the power of these systems, a detailed understanding of manybody effects is required, such as fluctuations, correlations, and entanglement. In this thesis, we seek to understand these observables in the context of macroscopic quantum tunneling. We quantify the macroscopic quantum tunneling dynamics, showing how interactions alter tunneling and quantum phase transitions modify nonequilibrium dynamics, providing a road maps of future experiments. The first experimental realization of meanfield interactions producing nonexponential decay of a tunneling BoseEinstein condensate has been achieved. We develop an effective semiclassical model which accounts for the repulsive atomatom interactions via an additional meanfield potential. This captures the 3D quantum tunneling via classical oscillations in an effective 1D trap and tunneling through a barrier with timedependent height due to meanfield interactions. Meanfield treatments work well for BoseEinstein condensates with negligible manybody effects, such as fragmentation, depletion, and fluctuations away from the mean. We show how a BoseEinstein condensate with nonnegligible fragmentation and depletion can be described with a renormalized meanfield. This suggest meanfield models are more widely applicable than previously thought, and that manybody physics may be hiding in such experiments and systems. Next, we explicitly look at the dynamics of manybody tunneling from a metastable trap, described by the BoseHubbard Hamiltonian in the superfluid quantum phase. The manybody physics are simulated using matrix product state methods, which allow exploration of lowlyentangled dynamics via data compression methods, and can calculate a wide range of quantum observables, like number fluctuations, correlations, and entanglement entropy. We compare manybody and meanfield dynamics, explicitly showing manybody tunneling times converge to meanfield tunneling times with increasing number of atoms in the system. We find rich dynamics with different time scales for the escape time, fluctuations, and quantum entropy in the system. With a firm grasp on the superfluid dynamics in the BoseHubbard Hamiltonian, we turn our attention to the superfluid to Mott insulating quantum phase transition, and understanding how the initial quantum phase alters macroscopic quantum tunneling. We examine this for both the doublewell and quantum escape systems. We find that the dynamics of tunneling are strongly dependent on the quantum phase of the ground state. Qualitatively, the superfluid regime has wavelike dynamics, while the Mott regime has particlelike dynamics, and near the critical point there is a mixture of the two. The dynamics of manybody observables, fluctuations and correlations, have distinct signatures of their quantum phases, fingerprints pointing to the quantum phase transition. Finally, we provide a road map for future macroscopic quantum tunneling experiments, in particular for two accessible trap configurations in both semiclassical and strongly interacting regimes. Using a semiclassical method, we study the gross features of macroscopic quantum tunneling in symmetric offset Gaussian barriers, and a linearly ramped Gaussian barrier. Because the tunneling probability depends exponentially on the barrier area, large, heavy, or many interacting atoms can have tunneling rates too slow to be experimentally viable. We show how to overcome this timescale issue, quantifying the time and length scales regarding macroscopic quantum tunneling of BoseEinstein condensates of rubidium, lithium, and sodium, deriving scaling laws for the various trap parameters; the experimental ``knobs''. Scaling laws clearly demonstrate when oscillations in the well or tunneling probabilities dominate. We find the emergence of meanfield islands inside the traps, resulting in multiple oscillations. In the strongly interacting regime, preliminary evidence is provided for pulsed and continuouswave regimes of a correlationbased atom laser utilizing macroscopic quantum tunneling in both barrier and interaction control.