Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation

Ogunkoya, Oluwadara; Kim, Joonho; Peng, Bo; Özgüler, A. Barış; Alexeev, Yuri

doi:10.1103/physreva.109.012426

Title: Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation

Journal Article · Mon Jan 22 00:00:00 EST 2024 · Physical Review A

DOI:https://doi.org/10.1103/physreva.109.012426· OSTI ID:2246733

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Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States). Superconducting Quantum Materials and Systems Center (SQMS)
Rigetti Computing, Berkeley, CA (United States)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Argonne National Laboratory (ANL), Argonne, IL (United States)

Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to $d$ -dimensional quantum units or qudits has opened new avenues for improving computational efficiency. Here, this paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, which may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our paper outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Argonne National Laboratory (ANL), Argonne, IL (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-07CH11359; AC02-06CH11357

OSTI ID:: 2246733

Report Number(s):: FERMILAB-PUB-23-486-SQMS; arXiv:2309.00740; oai:inspirehep.net:2693502

Journal Information:: Physical Review A, Vol. 109, Issue 1; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation

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