Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections

Abstract

We determine the universal law for fidelity decayin quantum computations of complex dynamics in presenceof internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied toquantum computations in presence of imperfections.The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales forreliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermi's golden rule which are well known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenientmethod for the quantum computation of the coarse-grained Wigner function is also proposed.

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