Classical training of conditional instantaneous quantum polynomial-time Born machines

arXiv:2611.05483v1 Announce Type: new Abstract: Instantaneous quantum polynomial-time (IQP) Born machines are attractive quantum generative models, as certain IQP circuit families are conjectured to be hard to sample, yet they can be trained classically. Previously proposed conditional IQP Born machines make the parameters of the diagonal layer condition dependent. We introduce conditional IQP Born machines, in which the condition is encoded in the input state and a single IQP unitary is shared across conditions. Efficient sampling and amplitude-ratio evaluation for the reference state entering the diagonal layer suffice to obtain unbiased classical estimates of a conditional maximum mean discrepancy objective and its gradients.