Quantum

Classical training of conditional instantaneous quantum polynomial-time Born machines

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Briefings

A new class of classical-trained conditional IQP Born machines was introduced, where the conditioning is encoded in the input state rather than the diagonal layer parameters. The research demonstrates that this approach can represent conditional families that diagonal conditioning cannot, using a single shared unitary across conditions. For the sixteen-qubit Curie-Weiss spin model, the conditional model achieves a mean total variation distance six times lower than diagonal conditioning while matching classical generative models with significantly more parameters. The study also reports successful classical training of these models up to 2048 qubits for reproducing magnetization profiles.

Key points

• Conditional IQP Born machines encode conditioning in the input state rather than diagonal layer parameters, enabling representation of families unattainable by diagonal conditioning.
• The sixteen-qubit Curie-Weiss spin model is the first case where a single conditional model captures magnetization transitions at held-out temperatures with superior fidelity.

Context

This research addresses the challenge of training quantum generative models for conditional generation, specifically for IQP circuit families that are conjectured to be hard to sample. The findings provide a method to achieve unbiased classical estimates of conditional objectives and gradients, extending existing IQP Born machine capabilities to conditional generation tasks.

Limitations

Results are limited to the sixteen-qubit Curie-Weiss spin model for conditional representation and up to 2048 qubits for magnetization profile reproduction. The study does not provide evidence for generalizability to larger systems or other physical models beyond the tested spin model.

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