Speaker
Description
Training quantum generative models with the maximum mean discrepancy (MMD) avoids explicit likelihood evaluation, but transfers a central design choice to the kernel. In quantum circuit Born machines over bitstrings, the commonly used Gaussian kernel is an isotropic function of Hamming distance. This kernel can be interpreted as a weighted mixture of Pauli-Z parity observables, with all parities of equal degree receiving the same weight. This is natural in the infinite-sample setting, but suboptimal when training is constrained by a finite observable budget. We propose Sparse Parity Search (SPS), a method for learning anisotropic MMD kernels from target samples. SPS first performs a Goldreich-Levin-inspired search to discover high-magnitude empirical Fourier coefficients on the Boolean hypercube. It then constructs a sparse target-adapted spectral distribution over the discovered parity masks and mixes it with an isotropic Gaussian floor. The resulting kernel remains characteristic while concentrating MMD weight on coordinate-specific observables that are expected to be useful during training.We demonstrate SPS in IQP-based generative modeling. On synthetic parity-check distributions, where the target Fourier spectrum is sparse and known, SPS recovers the relevant parity constraints and improves exact total variation distance over a local Gaussian MMD baseline at 12, 14, and 16 qubits under a matched operator budget. On 28-qubit bipartite graph datasets, SPS improves the generation of global structural features relative to isotropic MMD. These results show that learning anisotropic kernels from samples can make MMD training more effective by turning kernel choice into observable allocation.
| Topic | Quantum variational circuits and their applications |
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