Preparing quantum-many body scars on a quantum computer

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Gustafson, Erik J.
Li, Andy C. Y.
Khan, Abid
Kim, Joonho
Kurkcuoglu, Doga Murat
Alam, M. Sohaib
Rahmani, Armin
Iadecola, Thomas
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Orth, Peter
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Physics and Astronomy
Physics and astronomy are basic natural sciences which attempt to describe and provide an understanding of both our world and our universe. Physics serves as the underpinning of many different disciplines including the other natural sciences and technological areas.
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Ames National Laboratory

Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.

For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.

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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.
This is a pre-print of the article Gustafson, Erik J., Andy CY Li, Abid Kahn, Joonho Kim, Doga Murat Kurkcuoglu, M. Sohaib Alam, Peter P. Orth, Armin Rahmani, and Thomas Iadecola. "Preparing quantum-many body scars on a quantum computer." arXiv preprint arXiv:2301.08226 (2023). DOI: 10.48550/arXiv.2301.08226, Copyright 2023 The Authors. Posted with permission.
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