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

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 <math> <mi>d</mi> </math> -dimensional quantum units or qudits has opened new avenues for improving computational efficiency. 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.. Authors: Ogunkoya, Oluwadara [Fermilab] (ORCID:0000000294856656); Kim, Joonho [Rigetti Computing] (ORCID:0000000254083572); Peng, Bo [PNL, Richland] (ORCID:0000000242267294); Barış Özgüler, A. [Fermilab] (ORCID:0000000286708004); Alexeev, Yuri [Argonne] (ORCID:0000000150662254). DOE Contract: 89243024CSC000002; AC02-06CH11357; AC02-07CH11359; AC05-76RL01830. Subjects: 97 MATHEMATICS AND COMPUTING; quantum algorithms & computation; quantum circuits; quantum computation; quantum control; quantum error correction; spin dynamics