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Analog and digital adiabatic quantum annealing with oscillating transverse fields
Tang, Zhijie
Tang, Zhijie
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2021
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2023-04-14
Abstract
This thesis investigates both analog Quantum Annealing and digital Quantum Annealing with oscillating transverse field in solving hard optimization problems.
In the first part, we consider a range of unconventional modifications to Quantum Annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by “transverse field chaos” in larger systems, classical and quantum methods are steered toward a false local minimum. To go from this local minimum to the global minimum, all N spins must flip, making this problem exponentially difficult to solve. We numerically study this problem by using a variety of new methods from the literature: inhomogeneous driving, adding transverse couplers, and other types of coherent oscillations in the transverse field terms (collectively known as RFQA). We show that all these methods improve the scaling of the time to solution (relative to the standard uniform sweep evolution) in at least some regimes. Comparison of these methods could help identify promising paths towards a demonstrable quantum speedup over classical algorithms in solving some realistic problems with near-term quantum annealing hardware.
In the second part of the thesis, we explore a digitized version of RFQA inspired by the performance of RFQA in analog quantum computing. The digitization of Quantum Annealing is a combination of analog Quantum Annealing(QA) and Quantum Approximate Optimization Algorithm (QAOA). Digitized-QA can be applied to full-scale, fault-tolerant quantum algorithms. We apply the digitized version of RFQA and QA to various trial problems using classical numerical simulation and show that digitized-RFQA is a potentially promising tool in solving hard optimization problems and can be a new tool to complement QAOA and traditional digitized-QA.
In the third part of the thesis, for the preparation of an experiment, we investigate the 1D TFIM(transverse field ising model) and show that RFQA-D is able to accelerating the N-spin tunneling, the acceleration suggests that RFQA has the potential of mitigating the cost of minor embedding overhead.
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