Quantum circuits based on qutrits as a tool for solving systems of linear equations

TL;DR

This paper introduces a quantum circuit using qutrits designed specifically for solving three-variable linear systems, with potential generalization to larger systems, supported by numerical validation.

Contribution

It proposes a novel qutrit-based quantum circuit for solving three-variable linear equations, extending the capabilities of existing qubit-based methods.

Findings

Circuit correctly solves three-variable systems.

Method generalizes to systems with 3^n variables.

Numerical experiments verify the approach.

Abstract

Recently, it has been presented some algorithms and physical models which give prospects for construction of quantum computers capable to solve systems of linear equations. The common feature which is shared in these works is the use of qubits which allow to solve systems with $2^n$ variables. In this work we propose a quantum circuit based on qutrits architecture which directly allows for solving systems of equations with three variables. Proposed circuit can be easily generalized to those with $3^n$ variables. We also present some numerical experiments to verify the correctness of proposed solution.