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
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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
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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 BoseHubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to nonequilibrium quantum dynamics. 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Opensource practical intermediate representation for quantum and hybrid quantum algorithmsKapit, Eliot; Ayaz, Hakan; Aaen, Peter H.; Gong, Zhexuan (Colorado School of Mines. Arthur Lakes Library, 2023)The current noisy intermediatescale quantum (NISQ) era allows researchers to explore hybrid (quantumclassical) computing. Like classical computing, intermediate representations define an environment from the source code to the hardware backend. Classical computing has different supporting toolchains for Windows, Linux, and Mac systems. Interoperability across the sets of quantum compiler toolchains would be better for everyone. The practical intermediate representation of quantum (PIRQ) project is taking early steps toward fully opensource intermediate representation methods for all classical, full quantum, and hybrid algorithm systems. We use hybrid quantumclassical algorithms such as Variational Quantum Eigensolver (VQE) and a particular part of VQE, the Quantum Approximate Optimization Algorithm (QAOA). However, due to scattered compilation tools and asymmetric support, it is challenging to understand precisely how a hybrid quantumclassical algorithm is compiled, what that intermediate representation looks like, and how to run that intermediate representation on quantum/classical devices. This thesis discusses my work as part of the QEDC PIRQ project in collaboration with Adin Gitig, Daniel Mendez and company indivuduals feedbacks from Zapata, Quantiniuum, Microsoft, Ionq, and Quantum Circuits. The PIRQ aims to research useful quantum intermediate representation and current implementations. I’ve been working on this project actively since March. According to the goal of PIRQ, we developed an educational resource: a GitHub repository of compilation steps through the current hybrid quantumclassical compilation ecosystem. The educational repository is structured in modules, each introducing an aspect of compilation. The tutorials include examples in Open QASM, QIR, Q#, and python frameworks such as Qiskit. Topics include transpilation and optimization for quantum hardware and generating LLVM IR for quantum algorithms using QCOR. Module 1 is a condensed introduction to a standard classical compilation step in the classical compilation. Module 2 dives into tutorials centered around the IR for quantum algorithms to understand what would enable a practical IR for quantum algorithms in quantum devices. In module 3, we explore the emerging frontier of hybrid quantumclassical compilation. We are exploring five methods to create a hybrid intermediate representation: pyQIR, Rust implementation, QCOR implementation, Q#, and Intel quantum SDK. We hope these modules will motivate the community to contribute to more tutorials and develop hybrid quantum classical compilation as a critical building block for PIRQ. In this thesis, only two of these methods are used because other projects are still under construction to be opensource.

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.