# Theoretical Physics

**17 May 2017**

**Time:**15:00 to 16:00

**Location:**MNP Room

Theoretical Physics Seminar: Pietro Rotondo (Nottingham)

Multimodal cavity quantum electrodynamics with disorder and a connection with Hopfield neural networks

Abstract: The Dicke model is a paradigm in many-body quantum optics and its solution was firstly proposed for the single mode case by Hepp and Lieb in 1973 [1]. Recently quantum simulators based on cavity QED for the multimodal Dicke model with disorder have been proposed [2]. However in this case the exact solution of the model is not available and therefore little is known about this physical system in the thermodynamic limit. Using an approach inspired from Spin Glasses, I show that the multimode disordered Dicke model is equivalent to a quantum Hopfield neural network [3], the simplest model of associative memory [4]. Based on the exact calculation of the partition function, I propose variational ground states for the

system at zero temperature, which I conjecture to be exact in the thermodynamic limit. These ground states contain the information on the disordered qubit-photon couplings. Finally I briefly discuss the possible relevance of this class of quantum simulators for quantum computing purposes.

[1] K. Hepp and E. Lieb, Ann. Phys. 76, 360 (1973).

[2] S. Gopalakrishnan, B. Lev, and P. Goldbart, PRL 107, 277201 (2011); P. Strack and S. Sachdev, PRL107, 277202 (2011).

[3] J. J. Hopfield, PNAS 79, 2554 (1982).

[4] P. Rotondo, M. Cosentino Lagomarsino, G. Viola, PRL 114, 143601 (2015).

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