Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics

TYC and MMM Hub members collaborated on the recent paper 'Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics' which was published in Physical Review X

Simulating many interacting quantum particles is a problem at the heart of a broad range of key scientific challenges, from the promise of chemistry by computational design to manipulating the emergent properties of novel materials. The central quantum variable, the wave function, is, however, an exponentially complex object, with amplitudes associated with every possible classical arrangement of the particles in the system. Therefore, the history of advances in interacting quantum systems is often punctuated by the discovery of accurate and compact representations of these quantum states. We introduce a new representation of quantum states via a probabilistic, machine-learned model over the distribution of possible classical arrangements of particles. The central paradigm of our work stems from asking the following question: If we knew the amplitudes on a small number of these classical configurations, what is the optimal statistical model to infer the amplitudes on all other configurations, in order to define the true quantum state? We show that this “Gaussian process state” explicitly encompasses many other established wave-function forms in a highly compact manner, and we establish numerical algorithms to allow optimization of these chosen classical configurations in order to compactly find the most accurate state for a general interacting quantum system. This new framework has the potential to impact a diverse range of fields, from quantum-state tomography, which reconstructs quantum states from limited experimental measurements, to the computational modeling of quantum chemistry and condensed matter physics.

https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.041026

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