Control over the structure of interactions is essential for developing flexible quantum protocols. We couple an array of atomic ensembles to a driven optical cavity, creating an XY model. Using a magnetic field gradient and modulating the cavity field enables us to prune the naturally all-to-all connectivity of cavity-mediated interactions. We confirm these coupling graphs by direct measurements of two-point correlation functions. From the correlation measurements, we infer the structure and Euclidean embedding of the equivalent Hamiltonian with only local interactions. Example geometries include a Moebius ladder and a cylinder with sign-changing interactions.
This control of interactions can be leveraged to study a wide range of physical systems, including quantum gravity and quantum computation. We simulate spin systems relating quantum mechanics and gravity, inspired by a discretized formulation of the AdS/CFT correspondence. We show that the states generated by the cavity dynamics map to low-energy states of the programmed XY model. Finding the ground state of the XY Hamiltonian is an NP-hard problem, and these highly-programmable interactions open avenues towards spin-glass physics and physically-encoded computation.
|Presenter name||Avikar Periwal|
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