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Description
This work introduces Transform-Graph Quantum Generative Models, a generalised family of classically trainable, quantum-deployable generative models denoted M(T,G,K). The framework extends recent Fourier-DQGM approaches, which avoid the fixed spectral bias of MMD-trained QCBMs by using likelihood-like training with a Parseval hidden-register estimator. While Fourier-DQGM makes training tractable, it fixes the readout to the Fourier transform, restricts the interaction structure to a visible-hidden bipartite graph, and uses a fixed Monte Carlo estimator budget. The proposed model relaxes these choices through three controllable design axes: the transform/readout basis T, the interaction/factor graph G, and the hidden-sample budget K.
The method defines a transform-dependent training likelihood as a visible all-zero marginal with hidden qubits traced out. A transform-graph Parseval identity rewrites this marginal as an expectation over hidden bitstrings, enabling scalable Monte Carlo estimation. Transform columns are decomposed into branch sums, allowing Hartley, Chebyshev, and Haar readouts to be trained using transform-specific Parseval estimators. The product factorisation of the original model is also generalised to bounded-width tensor contractions, preserving tractability when the conditioned visible graph has bounded treewidth or pathwidth. A finite-K analysis shows that although the probability estimator is unbiased, the negative log-likelihood has a positive bias approximately equal to rho/(2K).
Preliminary experiments validate all three axes. Bounded graph contractions improve structured targets and high-order Walsh-Hadamard matching; adaptive-K and bias-corrected losses improve rare-event robustness; and non-Fourier transforms provide useful target-dependent inductive biases.
| Topic | Quantum variational circuits and their applications |
|---|---|
| Additional Topic | Tensor methods and quantum-inspired machine learning |