A Quantum Hopfield Neural Network. (arXiv:1710.03599v2 [quant-ph] UPDATED)

Quantum computing allows for the potential of significant advancements in
both the speed and the capacity of widely-used machine learning techniques.
Here we employ quantum algorithms for the Hopfield network, which can be used
for pattern recognition, reconstruction, and optimization as a realization of a
content addressable memory system. We show that an exponentially large network
can be stored in a polynomial number of quantum bits by encoding the network
into the amplitudes of quantum states. By introducing a new classical technique
for operating the Hopfield network, we can leverage quantum algorithms to
obtain a quantum computational complexity that is logarithmic in the dimension
of the data. This potentially yields an exponential speed-up in comparison to
classical approaches. We also present an application of our method as a genetic
sequence recognizer.

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