Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation

TL;DR

This paper investigates algebraic relations like the Yang-Baxter-like equation to optimize and compress qudit-based quantum circuits, with a focus on spin-1 Hamiltonian simulation, aiming to improve circuit fidelity and efficiency.

Contribution

It introduces a turnover relation for three-qutrit propagators and explores its potential generalization to higher-dimensional circuits, advancing qudit-based quantum computing techniques.

Findings

Derived the turnover relation for three-qutrit propagators.

Proposed methods for circuit compression using algebraic relations.

Analyzed potential for generalizing relations to higher dimensions.

Abstract

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. 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, that 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 work 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.