Expressive Equivalence of Classical and Quantum Restricted Boltzmann Machines - Paper Implementation Challenge

[musfarmuhamed]

Paper Link

arXiv:2502.17562v1

Summary

This paper introduces semi-quantum restricted Boltzmann machines (sqRBMs), a hybrid quantum-classical model that combines:

• Commuting Pauli-Z terms on visible units (classical data).
• Non-commuting Pauli-X/Y/Z terms on hidden units (quantum interactions).
• Analytical gradients and 3× fewer hidden units than classical RBMs for equivalent expressivity.

Key contributions:

1. Closed-form probabilities and gradients for sqRBMs.
2. Theoretical proof of expressive equivalence: sqRBM_{n,m} ≡ RBM_{n,3m}.
3. Numerical validation on parity/cardinality datasets.

Implementation Tasks

1. Model Hamiltonian Encoding

   • Define visible units with Pauli-Z fields.
   • Implement non-commuting Pauli-X/Y/Z terms for hidden units.
   • Add parameterized Z⊗X/Y/Z couplings between visible and hidden units.

2. Gibbs State Preparation

   • Use variational thermalization or Trotterization to approximate e^{-βH}/Z.
   • Optimize circuit depth for NISQ compatibility (leverage Classiq’s synthesis engine).

3. Gradient Computation

   • Implement analytical gradients from Propositions 2–3 (closed-form expressions).
   • Integrate with Classiq’s parameter-shift/autodiff tools.

4. Training Loop

   • Hybrid workflow: Quantum sampling + classical optimization (e.g., AMSGrad).
   • Reproduce parity/cardinality dataset experiments (Fig. 3/4 in paper).

5. Benchmarking

   • Compare sqRBM vs. classical RBM resource requirements (hidden units, parameters).
   • Report TVD/KL divergence metrics.

[TomerGoldfriend]

Sounds good @musfarmuhamed, from a quick look it seems like you will have to implement a Gibbs state preparation as part of the algorithm. This is a non-trivial task in itself :-) .

Please note that we accept high-quality implementations in our repository and will be glad to accept a contribution that meets our standards.
Feel free to contact the community if you have any questions.

Good luck!