Semiclassical Approach to Classical Simulation of Quantum Annealers

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Quantum mechanics governs the behavior of the microscopic world, and its rules are very different from the laws of physics that are most familiar from everyday life. A scientific challenge of the 21st century is to harness the unique features of quantum mechanics for new technologies. For example, a computer that works on the basis of quantum logic would offer speed-ups and other advantages when compared with familiar classical computers, at least for some nearly intractable computational problems. Another type of machine called a quantum annealer can be used to solve optimization problems. While not a full-fledged quantum computer, a quantum annealer uses tunneling and entanglement during its operation, and its advantages over conventional machines is a topic of much current research. This project will attempt to show that the restrictions present in current quantum annealers mean that these machines are not yet sufficiently quantum mechanical to provide a fundamental computational advantage over conventional computation methods. If successful, this work will make clear that proposed modifications to current annealers, which are technologically feasible, are necessary for these devices to provide useful improvements over conventional computing approaches. If this claim is not proven, this work may provide insights into when current quantum annealers can be expected to outperform conventional computers.Quantum computation promises advantages over classical computation for certain problems. However, the experimental obstacles to the construction of a large scale quantum computer are formidable. Quantum annealing is an intermediate approach to obtaining some quantum advantage, and over the last decade it has been implemented on a reasonably large scale. Quantum annealers solve optimization problems, and there is experimental evidence for quantum effects such as tunneling and entanglement during their operation. A general theory of when these machines provide a quantum advantage is absent, but because of the existence of actual hardware a large body of empirical knowledge is accumulating about their operation. This work will address whether they can provide a uniquely quantum advantage over classical approaches. The project will address the following question for quantum annealers: Is there a local hidden variable theory that describes the operation of all current quantum annealing hardware? Theoretical tools to address this question include Wigner functions for discrete systems that give a description in terms of quasi-probabilities that sum to one, but which may be negative. When all the quasi-probabilities associated with states, operations and measurements are positive, the system admits a completely classical hidden variable description. This team will investigate whether such a positive, classical description can be accurate for quantum annealers.