Fig. 1: The hybrid training procedures we propose in this work.
From: The Born supremacy: quantum advantage and training of an Ising Born machine
We have a quantum generator along with auxiliary circuits used to compute the gradient of the various cost functions with respect to the parameters. The training procedure proceeds as follows. First, the QCIBM is sampled from N times via measurements. These samples, along with M data samples y ~ π(y), are used to evaluate a cost function, \({\cal{L}}_B\), where B ∈ {MMD, SD, SHD} is one of the efficiently computable cost functions. For each updated parameter, θk, two parameter-shifted circuits are also ran to generate samples, a, b ~ pθ±, which are used to compute the corresponding gradients, \(\partial _\theta {\cal{L}}_B\). For all costs functions and gradients, either a kernel (if a quantum kernel is used, the circuit in this figure must be run) is computed for each pair of samples (as is the case for MMD and SD) or an optimal transport cost function is evaluated (as is the case for SHD).
