Expressibility of the alternating layered ansatz for quantum computation

Kouhei Nakaji and Naoki Yamamoto

Department of Applied Physics and Physico-Informatics & Quantum Computing Center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama, 223-8522, Japan

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The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.

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[2] Tyler Volkoff and Patrick J. Coles, "Large gradients via correlation in random parameterized quantum circuits", Quantum Science and Technology 6 2, 025008 (2021).

[3] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik, "Noisy intermediate-scale quantum (NISQ) algorithms", arXiv:2101.08448.

[4] Zoë Holmes, Kunal Sharma, M. Cerezo, and Patrick J. Coles, "Connecting ansatz expressibility to gradient magnitudes and barren plateaus", arXiv:2101.02138.

[5] Oleksandr Kyriienko, Annie E. Paine, and Vincent E. Elfving, "Solving nonlinear differential equations with differentiable quantum circuits", arXiv:2011.10395.

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[8] Joe Gibbs, Kaitlin Gili, Zoë Holmes, Benjamin Commeau, Andrew Arrasmith, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, "Long-time simulations with high fidelity on quantum hardware", arXiv:2102.04313.

[9] Tobias Haug, Kishor Bharti, and M. S. Kim, "Capacity and quantum geometry of parametrized quantum circuits", arXiv:2102.01659.

[10] Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, and Kishor Bharti, "NISQ Algorithm for Hamiltonian Simulation via Truncated Taylor Series", arXiv:2103.05500.

[11] Joonho Kim, Jaedeok Kim, and Dario Rosa, "Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems", arXiv:2010.00157.

[12] Andrew Arrasmith, Zoë Holmes, M. Cerezo, and Patrick J. Coles, "Equivalence of quantum barren plateaus to cost concentration and narrow gorges", arXiv:2104.05868.

The above citations are from SAO/NASA ADS (last updated successfully 2021-05-06 16:24:56). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-05-06 16:24:54).