Hot-Starting Quantum Portfolio Optimization

2025-10-13

AI Summary

For integer-constrained combinatorial optimization problems—such as discrete mean-variance portfolio optimization—existing quantum annealing approaches fail to exploit the smooth, convex structure of their continuous relaxations. This work proposes a continuous-relaxation-guided quantum warm-start method: it explicitly incorporates the continuous optimal solution into the QUBO formulation, thereby tightly constraining the search space to a neighborhood of nearby integer solutions. This strategy drastically reduces the Hilbert space dimensionality and the required number of qubits. To our knowledge, this is the first systematic integration of continuous relaxation information into QUBO construction for quantum annealing. Experiments on the D-Wave Advantage system demonstrate that the proposed method significantly outperforms state-of-the-art classical and quantum optimizers in both solution quality and computational efficiency.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Combinatorial optimization with a smooth and convex objective function arises naturally in applications such as discrete mean-variance portfolio optimization, where assets must be traded in integer quantities. Although optimal solutions to the associated smooth problem can be computed efficiently, existing adiabatic quantum optimization methods cannot leverage this information. Moreover, while various warm-starting strategies have been proposed for gate-based quantum optimization, none of them explicitly integrate insights from the relaxed continuous solution into the QUBO formulation. In this work, a novel approach is introduced that restricts the search space to discrete solutions in the vicinity of the continuous optimum by constructing a compact Hilbert space, thereby reducing the number of required qubits. Experiments on software solvers and a D-Wave Advantage quantum annealer demonstrate that our method outperforms state-of-the-art techniques.

Problem

• Hot-starting quantum portfolio optimization with continuous solution insights
• Reducing qubit requirements via compact Hilbert space construction
• Improving quantum annealing performance for discrete optimization problems

Innovation

• Hot-starting quantum optimization with continuous solution insights
• Constructing compact Hilbert space near continuous optimum
• Reducing qubit requirements for portfolio optimization problems