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arXiv:2501.08418

CVaR-Based Variational Quantum Optimization for User Association in Handoff-Aware Vehicular Networks

Zijiang Yan, Zhou, Hao, Jianhua Pei, Aryan Kaushik, Hina Tabassum, Ping Wang

Published Jan 14, 2025• 0 citations
arXivHTMLPDF

Abstract

Efficient resource allocation is essential for optimizing various tasks in wireless networks, which are usually formulated as generalized assignment problems (GAP). GAP, as a generalized version of the linear sum assignment problem, involves both equality and inequality constraints that add computational challenges. In this work, we present a novel Conditional Value at Risk (CVaR)-based Variational Quantum Eigensolver (VQE) framework to address GAP in vehicular networks (VNets). Our approach leverages a hybrid quantum-classical structure, integrating a tailored cost function that balances both objective and constraint-specific penalties to improve solution quality and stability. Using the CVaR-VQE model, we handle the GAP efficiently by focusing optimization on the lower tail of the solution space, enhancing both convergence and resilience on noisy intermediate-scale quantum (NISQ) devices. We apply this framework to a user-association problem in VNets, where our method achieves 23.5% improvement compared to the deep neural network (DNN) approach.

DOI
10.48550/arxiv.2501.08418

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Efficient resource allocation is essential for optimizing various tasks in wireless networks, which are usually formulated as generalized assignment problems (GAP). GAP, as a generalized version of the linear sum assignment problem, involves both equality and inequality constraints that add computational challenges. In this work, we present a novel Conditional Value at Risk (CVaR)-based Variational Quantum Eigensolver (VQE) framework to address GAP in vehicular networks (VNets). Our approach leverages a hybrid quantum-classical structure, integrating a tailored cost function that balances both objective and constraint-specific penalties to improve solution quality and stability. Using the CVaR-VQE model, we handle the GAP efficiently by focusing optimization on the lower tail of the solution space, enhancing both convergence and resilience on noisy intermediate-scale quantum (NISQ) devices. We apply this framework to a user-association problem in VNets, where our method achieves 23.5% improvement compared to the deep neural network (DNN) approach.
Efficient resource allocation is essential for optimizing various tasks in wireless networks, which are usually formulated as generalized assignment problems (GAP). GAP, as a generalized version of the linear sum assignment problem, involves both equality and inequality constraints that add computational challenges. In this work, we present a novel Conditional Value at Risk (CVaR)-based Variational Quantum Eigensolver (VQE) framework to address GAP in vehicular networks (VNets). Our approach leverages a hybrid quantum-classical structure, integrating a tailored cost function that balances both objective and constraint-specific penalties to improve solution quality and stability. Using the CVaR-VQE model, we handle the GAP efficiently by focusing optimization on the lower tail of the solution space, enhancing both convergence and resilience on noisy intermediate-scale quantum (NISQ) devices. We apply this framework to a user-association problem in VNets, where our method achieves 23.5% improvement compared to the deep neural network (DNN) approach.
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.
Efficient resource allocation is essential for optimizing various tasks in wireless networks, which are usually formulated as generalized assignment problems (GAP). GAP, as a generalized version of the linear sum assignment problem, involves both equality and inequality constraints that add computational challenges. In this work, we present a novel Conditional Value at Risk (CVaR)-based Variational Quantum Eigensolver (VQE) framework to address GAP in vehicular networks (VNets). Our approach leverages a hybrid quantum-classical structure, integrating a tailored cost function that balances both objective and constraint-specific penalties to improve solution quality and stability. Using the CVaR-VQE model, we handle the GAP efficiently by focusing optimization on the lower tail of the solution space, enhancing both convergence and resilience on noisy intermediate-scale quantum (NISQ) devices. We apply this framework to a user-association problem in VNets, where our method achieves 23.5% improvement compared to the deep neural network (DNN) approach.
We propose a slack-free penalty formulation for constrained binary optimization that eliminates auxiliary slack variables and preserves the feasibility structure of the original problem. The proposed approach introduces a nonlinear custom penalty function to enforce inequality constraints directly in the objective function. To address the computational challenges associated with evaluating nonlinear penalties in variational quantum algorithms, we employ the finite-sampling method that avoids the exponential complexity required by exact expectation computation. Furthermore, we integrate the Conditional Value-at-Risk (CVaR) objective to improve optimization robustness and guide the search toward high-quality solutions. The proposed framework is evaluated on instances of the multi-dimensional knapsack problem, a classical benchmark in combinatorial optimization. We showcase that the proposed custom-penalty formulation combined with CVaR sampling achieves improved optimality gaps and more consistent performance compared with conventional slack-based QUBO formulations. We also tested our method on the Quantinuum H2 quantum hardware, demonstrating the possibilities of training small-sized VQE on noisy trapped-ion quantum computers. The results suggest that careful penalty design can play a critical role in enabling quantum and hybrid quantum-classical algorithms for constrained optimization problems that arise in operations research.
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks, including solving optimization problems. Nonetheless, optimization problems with constraints may not have been handled in a disciplined fashion thus far. To address this gap, this work proposes a hybrid quantum-classical algorithmic paradigm termed the variational quantum eigensolver with constraints (VQEC) that extends the celebrated VQE to handle optimization with constraints. As with the standard VQE, the vector of optimization variables is captured by the state of a variational quantum circuit (VQC). To deal with constraints, VQEC optimizes a Lagrangian function classically over both the VQC parameters as well as the dual variables associated with constraints. To comply with the quantum setup, variables are updated via a perturbed primal-dual method leveraging the parameter shift rule. Among a wide gamut of potential applications, we showcase how VQEC can approximately solve quadratically constrained binary optimization problems, find stochastic binary policies satisfying quadratic constraints on the average and in probability, and solve large-scale linear programs over the probability simplex. Under an assumption on the error for the VQC to approximate an arbitrary probability mass function, we provide bounds on the optimality gap attained by a VQC. Numerical tests on a quantum simulator investigate the effect of various parameters and corroborate that VQEC can generate high-quality solutions.
Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs' collision avoidance model.