Differentiable Learning of Quantum Circuit Born Machine

TL;DR

This paper introduces a gradient-based training algorithm for quantum circuit Born machines, enabling efficient generative modeling on near-term quantum devices with potential quantum advantages.

Contribution

It develops a novel differentiable learning method using kernelized maximum mean discrepancy loss for quantum generative models, suitable for implementation on current quantum hardware.

Findings

Effective training of quantum circuits for generative tasks

Demonstrated modeling of Bars-and-Stripes and Gaussian mixtures

Highlighted importance of circuit depth and optimization techniques

Abstract

Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. One can efficiently draw samples from the quantum circuits via projective measurements on qubits. However, similar to the leading implicit generative models in deep learning, such as the generative adversarial networks, the quantum circuits cannot provide the likelihood of the generated samples, which poses a challenge to the training. We devise an efficient gradient-based learning algorithm for the quantum circuit Born machine by minimizing the kerneled maximum mean discrepancy loss. We simulated generative modeling of the Bars-and-Stripes dataset and Gaussian mixture distributions using deep quantum circuits. Our experiments show the importance of circuit depth and gradient-based optimization algorithm. The proposed learning algorithm is runnable on near-term quantum device and can exhibit quantum advantages for generative modeling.