Efficient Variational Quantum Algorithms for the Generalized Assignment Problem

TL;DR

This paper introduces VQGAP, a hybrid quantum-classical algorithm that efficiently solves the Generalized Assignment Problem by reducing quantum resource requirements while maintaining performance.

Contribution

VQGAP is a novel variational quantum algorithm that decouples qubits from problem variables, reducing circuit complexity for solving GAP on NISQ devices.

Findings

VQGAP performs similarly to VQE in simulations.

VQGAP reduces qubit count and circuit depth.

Effective on both noiseless and noisy simulations.

Abstract

Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale Quantum (NISQ) devices, hybrid quantum-classical approaches, specifically Variational Quantum Algorithms (VQAs) like the Variational Quantum Eigensolver (VQE), promises to be effective approaches to solve real-world optimization problems. This paper proposes an approach, named VQGAP, designed to efficiently solve the GAP by optimizing quantum resources and reducing the required parametrized quantum circuit width with respect to standard VQE. The main idea driving our proposal is to decouple the qubits of ansatz circuits from the binary variables of the General Assignment Problem, by providing encoding/decoding functions transforming the solutions generated by ansatze in the limited quantum space in feasible solutions in the problem variables space, by exploiting the constraints of the problem. Preliminary results, obtained through both noiseless and noisy simulations, indicate that VQGAP exhibits performance and behavior very similar to VQE, while effectively reducing the number of qubits and circuit depth.