Practical applications of machine learning to quantum computing and quantum simulation
AuthorLidiak, Alexander G.
Keywordsautoregressive artificial neural network variational ground-state search
matrix product operator supervised quantum state tomography
nonlinear unsupervised learning
quantum many-body physics
quantum optimal control - pulse optimization for fast 2-qubit gates
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AbstractThe understanding of quantum many-body 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 many-body systems and is further developed to allow GPU accelerated computing. Second, a machine learning based quantum optimal control algorithm is developed to design speed-optimized 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 non-trivial quantum phases and is applicable to state-of-art 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 one-dimensional noisy quantum computers. Each of these achievements is integral to the development of quantum technologies in realistic settings.
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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 Bose-Hubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to non-equilibrium quantum dynamics. 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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 Trotter-based time evolution scheme. We quantify the entanglement and complexity generated by 13 next-nearest 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 complexity-generating rule out of the 13 rules tested, verifying our hypothesis that only Goldilocks rules are complexity generating. 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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 Kohn-Sham 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 bulk-crystal 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 many-body dynamics in Bose-Einstein 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, many-body 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 many-body 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 non-equilibrium dynamics, providing a road maps of future experiments. The first experimental realization of mean-field interactions producing non-exponential decay of a tunneling Bose-Einstein condensate has been achieved. We develop an effective semi-classical model which accounts for the repulsive atom-atom interactions via an additional mean-field potential. This captures the 3D quantum tunneling via classical oscillations in an effective 1D trap and tunneling through a barrier with time-dependent height due to mean-field interactions. Mean-field treatments work well for Bose-Einstein condensates with negligible many-body effects, such as fragmentation, depletion, and fluctuations away from the mean. We show how a Bose-Einstein condensate with non-negligible fragmentation and depletion can be described with a renormalized mean-field. This suggest mean-field models are more widely applicable than previously thought, and that many-body physics may be hiding in such experiments and systems. Next, we explicitly look at the dynamics of many-body tunneling from a meta-stable trap, described by the Bose-Hubbard Hamiltonian in the superfluid quantum phase. The many-body physics are simulated using matrix product state methods, which allow exploration of lowly-entangled dynamics via data compression methods, and can calculate a wide range of quantum observables, like number fluctuations, correlations, and entanglement entropy. We compare many-body and mean-field dynamics, explicitly showing many-body tunneling times converge to mean-field 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 Bose-Hubbard 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 double-well 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 wave-like dynamics, while the Mott regime has particle-like dynamics, and near the critical point there is a mixture of the two. 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