Variational Quantum Thermalization and the Future of Quantum Thermodynamics

Rayleigh-Ritz method minimizes the energy of the trial wave function with respect to a given Hamiltonian provided each wave function is normalized. One can classically optimize this set of parameters which parametrize our trial wave function, such that the loss function represented by the free energy of the system is minimized.
Loss function for the VQT, parametrized by θ and ϕ. Source: https://arxiv.org/pdf/1910.02071.pdf
An abstraction of the full quantum circuit used to implement VQT. We prepare an initial density matrix parametrized by θ and ϕ. We then classically vary both parameters in order to minimize the loss function, using the quantum computer only for calculating the expectation value given the parametrized pure state that is being output based on some classical probability distribution pθ(Ψ). Source: https://arxiv.org/pdf/1910.02071.pdf
Visualization of the target state density matrix for the 2D XY model.
Loss History and Fidelity of the VQT Algorithm for the 2D XY model for 100 epochs.

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Deep Prasad

Deep Prasad

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CEO of ReactiveQ, BASc. Industrial Engineering ’18,University of Toronto, Quantum Computing and Runiversic Researcher. The world belongs to the curious.