Preparing exact eigenstates of the open XXZ chain on a quantum computer

Van Dyke, John S.; Barnes, Edwin; Economou, Sophia E.; Nepomechie, Rafael I.

doi:10.1088/1751-8121/ac4640

Title: Preparing exact eigenstates of the open XXZ chain on a quantum computer

Journal Article · 12 January 2022 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ac4640 · OSTI ID:1979447

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Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); OSTI
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Univ. of Miami, Coral Gables, FL (United States)

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. Here, we formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of $$(^{L}_{M})$$ $$2^{M} M!$$ terms, the algorithm requires L+M²+2M qubits.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States); Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0012704; SC0019199

OSTI ID:: 1979447

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 5 Vol. 55; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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