Differentiable Learning of Quantum Circuit Born Machine

By Jin-Guo Liu, Lei Wang. Physical Review A, 2018

315 citations recorded by the source corpus.

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 the gradient-based optimization algorithm. The proposed learning algorithm is runnable on near-term quantum device and can exhibit quantum advantages for probabilistic generative modeling.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/a66d4cb2ca4a59d6d39c00f7d4fcf0b2175a1ddf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

Citations in the corpus

Evaluating analytic gradients on quantum hardware (2018, background): “[11] Jin-Guo Liu and Lei Wang, “Differentiable learning of quantum circuit born machine,” (2018), arxiv:1804.”
General parameter-shift rules for quantum gradients (2021, background): “de tion [17, 18], and variational quantum machine learning [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31].”
Quantum Generative Adversarial Networks for learning and loading random distributions (2019, methodology): “[52] J.”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, background): “[59] the authors show how to train Born machines using dif-”
Effect of data encoding on the expressive power of variational quantum-machine-learning models (2020, background): “A lot of work has been done to understand the practical details of this approach, leading to useful training strategies [3, 7, 8] and ways to emulate and extend classical machine learning methods [2, 9–12].”
Barren plateaus in variational quantum computing (2024, unknown): “Thus, noise leads to an extended PQC V θ that can act in a larger space, which could be exponentially large (although not necessarily) and thus substantially aggravates the curse of dimensionality.”
Robust data encodings for quantum classifiers (2020, background): “[29] J.”
Quantum machine learning models are kernel methods (2021, background): “The natural shape of this analogy sparked more research in the past years, for example on training generative quantum models [9], constructing kernelised machine learning models [10], understanding the separation between the computational complexity of quantum and classical machine learning [11, 12]”
Variational quantum algorithms (2020, methodology): “, this corresponds then to a quantum circuit Born machine [145].”