Quantum Scrambling Born Machine

TL;DR

This paper introduces a Quantum Scrambling Born Machine that uses a fixed entangling unitary as a scrambling reservoir, enabling efficient quantum generative modeling with competitive performance to classical models.

Contribution

It proposes a novel quantum generative model leveraging fixed entangling unitaries and variational Hamiltonian training, demonstrating effectiveness across different entangling schemes.

Findings

Near-Haar entanglement suffices for learning target distributions.

Model performance is robust to the microscopic details of the entangler.

Variational Hamiltonian approach achieves competitive results with classical models.

Abstract

Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary -- acting as a scrambling reservoir -- provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries -- a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians -- and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.