5.4 Quantum Annealing and Boltzmann Sampling
The application of quantum annealing to Boltzmann sampling is based on the direct correspondence between the RBM energy function given by (5.2.4) and the Hamiltonian in quantum annealing. Recall from Chapter 2 that quantum annealing is based on the principles of adiabatic evolution from the initial state at t = 0 given by a Hamiltonian H0 to a final state at t = T given by a Hamiltonian HF , such that the system Hamiltonian at time t ∈[0,T] is given by
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where r(t) decreases from 1 to 0 as t goes from 0 to T. An ideal adiabatic evolution scenario envisages the system always staying in the ground state of H(t): if the system starts in the ground state of H0 and the evolution proceeds slowly enough to satisfy the conditions of the quantum adiabatic theorem (Chapter 2), then the system will end up in the ground state of HF .
In practice, existing quantum annealing...
