Differentiable Learning of Quantum Circuit Born Machine
This work addresses a key training bottleneck for quantum generative models, which could impact researchers in quantum machine learning, though it appears incremental as it adapts classical gradient methods to quantum settings.
The authors tackled the challenge of training quantum circuit Born machines, which lack likelihood estimates, by developing a gradient-based learning algorithm using kerneled maximum mean discrepancy loss. They demonstrated its effectiveness on the Bars-and-Stripes dataset and Gaussian mixtures, showing improved performance with deeper circuits and gradient optimization, and claimed it is runnable on near-term quantum devices with potential quantum advantages.
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.