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Universal laws for fidelity decay

Quantum computers, relying on the weird logics of the quantum world, can be much faster than any classical machine, since they perform, so to speak, all the calculations at once. However, their construction is rather challenging, since they are prone to errors and decoherence. The EDIQIP project addressed an important question: what is the influence of static imperfections in computer hardware (parasitic coupling between qubits, imperfections in qubit energies). It determined a universal law, based on random matrix theory invented by Wigner for complex nuclei and atoms, for the computation fidelity decay induced by internal static imperfections.

The theoretical predictions were confirmed by extensive numerical simulations of a quantum algorithms. The decay law provides a transition between exponential and Gaussian behaviours and is characterized by two time-scales analogous to the Thouless and Heisenberg times for probability decay in mesoscopic systems. These studies establish the universal accuracy bounds for quantum computation in presence of residual static couplings between qubits. They are essential to estimate the individual gates fidelity required for a large scale quantum computation. The universal fidelity decay law induced by dissipative effects have also been determined and compared with the effects of static imperfections.

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