Expressive power of parametrized quantum circuits

By Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, Dacheng Tao. Physical Review Research, 2020

326 citations recorded by the source corpus.

Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addition, PQCs equipped with ancillary qubits for post-selection have even stronger expressive power than those without post-selection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semi-supervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical experiments using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5aac8750282d068d2a5e51c1115fdf3237fec185

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Pin-Yu Chen

Citations in the corpus

Quantum variational algorithms are swamped with traps (2022, unknown): “[23] Surbhi Goel, Aravind Gollakota, Zhihan Jin, Sushrut Karmalkar, and Adam Klivans.”
Variational Quantum Circuits for Deep Reinforcement Learning (2019, background): “More specifically, we take the advantages of quantum entanglement [20, 21] in quantum computing to reduce our model size into an essentially small number such that quantum algorithms can be realized on the available quantum platforms which are named as Noisy Intermediate-Scale Quantum machines (NISQ”
Parameterized quantum circuits as machine learning models (2019, background): “[74] Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, and Dacheng Tao, “The expressive power of parameterized quantum circuits,” arXiv preprint arXiv:1810.”