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What is Sampling and the Complexity of Nature about?

Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed probability distribution is therefore a natural technological application of quantum devices. In the research presented in this thesis, I investigate the complexity-theoretic and physical foundations of quantum sampling algorithms. I assess the computational power of natural quantum simulators and close loopholes in the complexity-theoretic argument for the classical intractability of quantum samplers (Part I). I shed light on how and under which conditions quantum sampling devices can be tested or verified in regimes that are not simulable on classical computers (Part II). Finally, I explore the computational boundary between classical and quantum computing devices (Part III). In particular, I develop efficiently computable measures of the infamous Monte Carlo sign problem and assess those measures both in terms of their practicability as a tool for alleviating or easing the sign problem and the computational complexity of this task. An overarching t

Author

Hangleiter, Dominik

Published

2020

Language

EN