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Algorithms and subroutines for quantum optimization
Grattan, George
Grattan, George
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2024
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Abstract
Quantum computing is a computing paradigm that leverages quantum mechanical phenomena to encode and manipulate information in ways that our current (classical) computers cannot. As of now there are only a handful of specific problems with a mathematically provable speedup over classical computing; however, there is some evidence suggesting that quantum computers could outperform classical computers in the realm of optimization. This thesis covers two quantum methods that make strides towards realizing quantum utility in the realm of optimization. The first is a quantum cooling algorithm dubbed the Relaxational Quantum Eigensolver (RQE) that uses ancillary qubits to engineer a cold bath used to remove energy and entropy from the qubits encoding our problem. By cleverly engineering this cold bath we can prepare approximate ground states in the face of depolarizing noise. Furthermore, we explore a new thermometry method that uses measurements of the thermalized ancillary qubits to characterize the optimality of our prepared states by estimating a temperature. This method will enable quantum scientists to probe and study a prepared quantum, state without directly measurement.
The second method enables an exponential speedup in Macroscopic Quantum Tunneling (MQT) which we have dubbed Symphonic Tunneling. This mechanism is new to the literature and has applications to quantum optimization, adiabatic quantum computing, and a potential realization of NISQ quantum utility.
Both methods will be valuable tools for both scientific and industrial applications of quantum optimization and simulation.
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