Local random quantum circuits are approximate polynomial-designs - numerical resultsReportar como inadecuado



 Local random quantum circuits are approximate polynomial-designs - numerical results


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We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary polyn-design F.G.S.L. Brandao et al., arXiv:1208.0692. Using a group theory formalism, spectral gaps that give a ratio of convergence to a given t-design are evaluated for a different number of qubits n up to 20 and degrees t t=2,3,4 and 5, improving previously known results for n=2 in the case of t=2 and 3. Their values lead to a conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases, only tells that a gap is closed. We compare our results to the another lower bounding technique, again showing that its results may not be tight.



Autor: Piotr Ćwikliński; Michał Horodecki; Marek Mozrzymas; Łukasz Pankowski; Michał Studziński

Fuente: https://archive.org/







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