Benchmark for the quantum-enhanced control of reversible dynamics. (arXiv:1706.04128v2 [quant-ph] UPDATED)

Controlling quantum systems is crucial for quantum computation and a variety
of new quantum technologies. The control is typically achieved by breaking down
the target dynamics into a sequence of elementary gates,whose description can
be stored into the memory of a classical computer. Here we explore a different
approach, initiated by Nielsen and Chuang, where the target dynamics is encoded
in the state of a quantum system, regarded as a "quantum program". We show that
quantum strategies based on coherent interactions between the quantum program
and the target system offer an advantage over all classical strategies that
measure the program and conditionally operate on the system. To certify the
advantage, we provide a benchmark that guarantees the successful demonstration
of quantum-enhanced programming in realistic experiments.

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