Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1
Hamiltonian Simulation
- URL: http://arxiv.org/abs/2309.00740v2
- Date: Wed, 20 Dec 2023 06:52:50 GMT
- Title: Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1
Hamiltonian Simulation
- Authors: Oluwadara Ogunkoya, Joonho Kim, Bo Peng, A. Bar{\i}\c{s} \"Ozg\"uler,
Yuri Alexeev
- Abstract summary: This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits.
As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation.
- Score: 6.082536657383077
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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