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Dicke simulators with emergent collective quantum computational abilities
Pietro Rotondo, Marco Cosentino Lagomarsino, Giovanni Viola
Abstract: Using an approach inspired from Spin Glasses, we show that the multimode disordered Dicke model is equivalent to a quantum Hopfield network. In the strong coupling regime both models have the same free-energy landscape, characterized by a fixed number of degenerate global minima. We propose variational ground-states for the system at zero temperature, which we conjecture to be exact in the thermodynamic limit. These ground-states contain the information on the disordered qubit-photon couplings. The proposed and partially realized quantum simulators in Cavity and Circuit QED suggest two intriguing physical implications of these results. First, once the qubit-photon couplings can be engineered, it should be possible to build pattern storing systems whose dynamics is governed by quantum laws. Second, we show with an example how such Dicke quantum simulators may be used as a solver of "hard" combinatorial optimization problems.