1 research outputs found
Training Quantum Boltzmann Machines with the -Variational Quantum Eigensolver
The quantum Boltzmann machine (QBM) is a generative machine learning model
for both classical data and quantum states. The training of the QBM consists of
minimizing the relative entropy from the model to the target state. This
requires QBM expectation values which are computationally intractable for large
models in general. It is therefore important to develop heuristic training
methods that work well in practice. In this work, we study a heuristic method
characterized by a nested loop: the inner loop trains the -variational
quantum eigensolver (-VQE) by Liu et al. (2021) to approximate the QBM
expectation values; the outer loop trains the QBM to minimize the relative
entropy to the target. We show that low-rank representations obtained by
-VQE provide an efficient way to learn low-rank target states, such as
classical data and low-temperature quantum tomography. We test the method on
both classical and quantum target data with numerical simulations of up to 10
qubits. For the cases considered here, the obtained QBMs can model the target
to high fidelity. The approach offers a valuable route towards variationally
training QBMs on near-term quantum devices.Comment: 9 pages, 11 figure