Quantum strategy stores isometry channels with n = Θ(1/√ε) queries for error ε, quadratic improvement over classical n = Θ(ε^{-1}).
Truncations of random unitary matrices
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abstract
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.
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Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
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Quantum Advantage in Storage and Retrieval of Isometry Channels
Quantum strategy stores isometry channels with n = Θ(1/√ε) queries for error ε, quadratic improvement over classical n = Θ(ε^{-1}).
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Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.