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Simulation of quantum mechanical systems is a major potential application of quantum computers. Indeed, the problem of simulating Hamiltonian dynamics was the original motivation for the idea of quantum computation.
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Measurement-device–independent quantum key distribution (MDIQKD) represents a valid alternative for quantum cryptography. It requires fewer assumptions for security than standard prepare-and-measure schemes, while its implementation is less demanding than fully device-independent protocols.
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A quantum gate between a flying optical photon and a single trapped atom
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Despite significant progress and efforts, lattice gauge theories remain to be challenging to be simulated on classical computers. A quantum simulator of U(1) lattice gauge theories can however be implemented with superconducting circuits. This allows, for instance, the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models.