Explorations in Quantum Pseudorandomness

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In analogy to the fundamental role that random numbers play in classical information theory, random quantum states and unitary operators are a key resource in quantum information science. Unfortunately, generating a random unitary transformation is intractably inefficient, motivating the investigation of a weaker notion of quantum pseudorandomness that may be achieved efficiently while remaining practically useful. In this program, fundamental properties and implications of quantum pseudorandomness will be explored from a mathematical, information-theoretic, and physical standpoint, by focusing on the generation of pseudorandomness using so-called random quantum circuits. Primary emphasis will be placed on (i) characterizing the behavior of random circuits under more general conditions than considered thus far; and (ii) performing a dedicated study of the effect of implementation errors and decoherence. In doing so, the bigger goal of understanding whether random quantum circuits may serve to model the dynamics of generic many-body quantum systems will be kept in mind, with anticipated connections to the field of quantum chaos.The scientific impact of this program will be twofold. First, a substantially improved understanding of the complexity involved in generating pseudorandom states and operators using random quantum circuits is expected to emerge. Beside providing a firm theoretical foundation for quantum information protocols that presume randomness as a resource, this could eventually find application in enhanced quantum algorithm design. Second, additional fundamental insights will also be gained on the emergence and characterization of apparent randomness in the properties of complex quantum systems. Intensive training on subjects at the cross-disciplinary boundary between quantum information theory, applied mathematics, and many-body physics will be provided to the graduate student supported by this grant.