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Optimal quantum learning of a unitary transformation · Around

2009

Optimal quantum learning of a unitary transformation

Bisio, A., Chiribella, G., D'Ariano, G. M. et al.

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We address the problem of learning an unknown unitary transformation from a finite number of examples.

The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum fidelity.
Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine), and subsequently retrieving it.
We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a "measure-and-rotate" retrieving.

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