Efficient Variational Quantum Algorithms for the Generalized Assignment Problem

2025-11-04

AI Summary

This paper addresses the NP-complete Generalized Assignment Problem (GAP) by proposing VQGAP—the first variational quantum algorithm tailored for NISQ devices. Methodologically, it introduces a lightweight encoding/decoding scheme that directly maps quantum states to feasible solutions satisfying all constraints; crucially, it decouples qubits from problem variables and exploits constraint structure to compress the solution-space representation, thereby fully covering the feasible region under limited quantum resources. Built upon the VQE framework, VQGAP integrates a custom parameterized quantum circuit with noise-robust optimization strategies. Simulation results demonstrate that, while achieving solution quality comparable to standard VQE, VQGAP reduces qubit count by approximately 60% and circuit depth by over 50%, significantly enhancing resource efficiency and hardware compatibility.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• Developing efficient quantum algorithms for NP-complete Generalized Assignment Problem
• Optimizing quantum resources and reducing circuit width in NISQ devices
• Transforming quantum solutions to feasible assignments using problem constraints

Innovation

• VQGAP optimizes quantum resources for GAP
• Decouples qubits from binary variables via encoding
• Reduces qubit count and circuit depth effectively