Hamiltonian Variational Ansatz Without Barren Plateaus

Chae-Yeun Park and Nathan Killoran

Xanadu, Toronto, ON, M5G 2C8, Canada

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Abstract

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed $textit{barren plateaus}$, has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

Popular summary

Variational quantum algorithms (VQAs) solve a target problem by optimizing the parameters of a quantum circuit. While VQAs are one of the most promising applications of a near-term quantum computer, the practical usefulness of VQAs is often questioned. One of the central issues is that quantum circuits with random parameters often have exponentially small gradients, limiting the trainability of the circuits. This problem, dubbed barren plateaus, has gained lots of interest recently, but a general solution is still unavailable. This work proposes a solution to the barren plateaus problem for the Hamiltonian variational ansatz, a type of quantum circuit ansatz widely studied for solving quantum many-body problems.

► BibTeX data

@article{Park2024hamiltonian, doi = {10.22331/q-2024-02-01-1239}, url = {https://doi.org/10.22331/q-2024-02-01-1239}, title = {Hamiltonian variational ansatz without barren plateaus}, author = {Park, Chae-Yeun and Killoran, Nathan}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1239}, month = feb, year = {2024}<br /> }

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Cited by

[1] Richard D. P. East, Guillermo Alonso-Linaje, and Chae-Yeun Park, “All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks”, arXiv:2309.07250, (2023).

[2] M. Cerezo, Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz, and Zoë Holmes, “Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing”, arXiv:2312.09121, (2023).

[3] Jiaqi Miao, Chang-Yu Hsieh, and Shi-Xin Zhang, “Neural network encoded variational quantum algorithms”, arXiv:2308.01068, (2023).

[4] Chukwudubem Umeano, Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko, “What can we learn from quantum convolutional neural networks?”, arXiv:2308.16664, (2023).

[5] Yaswitha Gujju, Atsushi Matsuo, and Rudy Raymond, “Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications”, arXiv:2307.00908, (2023).

[6] Chandan Sarma, Olivia Di Matteo, Abhishek Abhishek, and Praveen C. Srivastava, “Prediction of the neutron drip line in oxygen isotopes using quantum computation”, Physical Review C 108 6, 064305 (2023).

[7] J. Cobos, D. F. Locher, A. Bermudez, M. Müller, and E. Rico, “Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories”, arXiv:2308.03618, (2023).

[8] Julien Gacon, Jannes Nys, Riccardo Rossi, Stefan Woerner, and Giuseppe Carleo, “Variational Quantum Time Evolution without the Quantum Geometric Tensor”, arXiv:2303.12839, (2023).

[9] Han Qi, Lei Wang, Hongsheng Zhu, Abdullah Gani, and Changqing Gong, “The barren plateaus of quantum neural networks: review, taxonomy and trends”, Quantum Information Processing 22 12, 435 (2023).

[10] Zheng Qin, Xiufan Li, Yang Zhou, Shikun Zhang, Rui Li, Chunxiao Du, and Zhisong Xiao, “Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver”, arXiv:2307.10324, (2023).

[11] Yanqi Song, Yusen Wu, Sujuan Qin, Qiaoyan Wen, Jingbo B. Wang, and Fei Gao, “Trainability Analysis of Quantum Optimization Algorithms from a Bayesian Lens”, arXiv:2310.06270, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-02-01 10:14:56). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Hamiltonian variational ansatz without barren plateaus

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