Preparing quantum many-body scar states on quantum computers

Erik J. Gustafson1,2, Andy C. Y. Li1,2, Abid Khan1,3,4,5, Joonho Kim1,6, Doga Murat Kurkcuoglu1,2, M. Sohaib Alam1,4,5, Peter P. Orth1,7,8,9, Armin Rahmani10, and Thomas Iadecola1,7,8

1Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
2Fermi National Accelerator Laboratory, Batavia, IL, 60510, USA
3Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, United States 61801
4USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA, 94043, USA
5Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA, 94035, USA
6Rigetti Computing, Berkeley, CA, 94710, USA
7Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
8Ames National Laboratory, Ames, IA 50011, USA
9Department of Physics, Saarland University, 66123 Saarbrücken, Germany
10Department of Physics and Astronomy and Advanced Materials Science and Engineering Center, Western Washington University, Bellingham, WA 98225, USA

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Abstract

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.

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[1] Michael Iversen, Jens H. Bardarson, and Anne E. B. Nielsen, "Tower of two-dimensional scar states in a localized system", Physical Review A 109 2, 023310 (2024).

[2] Dong Yuan, Shun-Yao Zhang, and Dong-Ling Deng, "Exact quantum many-body scars in higher-spin kinetically constrained models", Physical Review B 108 19, 195133 (2023).

[3] Pierre-Gabriel Rozon and Kartiek Agarwal, "Broken unitary picture of dynamics in quantum many-body scars", Physical Review Research 6 2, 023041 (2024).

[4] Clement Charles, Erik J. Gustafson, Elizabeth Hardt, Florian Herren, Norman Hogan, Henry Lamm, Sara Starecheski, Ruth S. Van de Water, and Michael L. Wagman, "Simulating Z2 lattice gauge theory on a quantum computer", Physical Review E 109 1, 015307 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-26 14:29:42) and SAO/NASA ADS (last updated successfully 2024-05-26 14:29:43). The list may be incomplete as not all publishers provide suitable and complete citation data.