Quantum Computation as Geometry
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Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.
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Cited by 4 Pith papers
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Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry
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Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane...
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