Preparing quantum many-body scar states on quantum computers

Journal Article · Mon Nov 06 19:00:00 EST 2023 · Quantum

DOI:https://doi.org/10.22331/q-2023-11-07-1171· OSTI ID:2204909

Gustafson, Erik J. ^[1]; Li, Andy C. Y. ^[1]; Khan, Abid ^[2]; Kim, Joonho ^[3]; Kurkcuoglu, Doga Murat ^[1]; Alam, M. Sohaib ^[4]; Orth, Peter P. ^[5]; Rahmani, Armin ^[6]; Iadecola, Thomas ^[7]

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

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 2204909
• Alternate ID(s): OSTI ID: 2222450; OSTI ID: 1915402
• Journal Information: Quantum, Journal Name: Quantum Vol. 7; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
• Country of Publication: Austria
• Language: English