Variational Quantum Non-Orthogonal Optimization

TL;DR

This paper introduces a quantum optimization method encoding classical variables in non-orthogonal quantum states, reducing qubit requirements and enabling complex problem solving on current noisy quantum hardware.

Contribution

It proposes a novel non-orthogonal state encoding scheme combined with VQE to minimize qubit usage for large-scale optimization problems.

Findings

Successfully optimized polynomial of degree 8 with 15 variables using 15 qubits.

Demonstrated significant qubit reduction compared to traditional methods.

Showed potential for solving real-world optimization problems on current quantum hardware.

Abstract

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We develop the case of non-orthogonal qubit states, with individual qubits on the quantum computer handling more than one bit classical variable. Combining this idea with Variational Quantum Eigensolvers (VQE) and quantum state tomography, we show that it is possible to significantly reduce the number of qubits required by quantum hardware to solve complex optimization problems. We benchmark our algorithm by successfully optimizing a polynomial of degree 8 and 15 variables using only 15 qubits. Our proposal opens the path towards solving real-life useful optimization problems in today's limited quantum hardware.