Near-linear constructions of exact unitary 2-designs
نویسندگان
چکیده
منابع مشابه
Near-linear constructions of exact unitary 2-designs
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be implemented by quantum circuits consisting of Õ(n) elementary gates in logarithmic depth. This is essentially a quadratic improvement in size (and in width times ...
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When studying “random” operators it is essential to be able to integrate over the Haar measure, both analytically and algorithmically. Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). In particular, by replacing averages over the Haar measure by averages over a finite set, they allow applications in algorithms. We provide three equivalent d...
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Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). We prove a classic result the trace double sum inequality and use it to derive the fundamental symmetries of t-designs. As an alternate approach to deriving an asymptotically tight lower bound on the size of t-designs, we introduce a greedy algorithm for constructing designs. Unfortunately, w...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2016
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic16.9-10-1