Best practices for portfolio optimization by quantum computing, experimented on real quantum devices

Area of Science:

• Quantum Computing
• Computational Finance
• Optimization Algorithms

Background:

• Portfolio optimization faces scalability challenges with increasing market dimensions.
• Quantum computing offers a potential solution to overcome computational complexity in finance.
• Classical optimization methods struggle with large-scale, constrained quadratic problems.

Purpose of the Study:

• To solve the portfolio optimization problem using the Variational Quantum Eigensolver (VQE).
• To identify and define the optimal hyperparameters for VQE in portfolio optimization on real quantum computers.
• To assess the performance and scalability of VQE for financial applications.

Main Methods:

• Formulating the constrained quadratic portfolio optimization problem.
• Translating the problem into Quadratic Unconstrained Binary Optimization (QUBO) using binary encoding.
• Converting the QUBO problem into an Ising Hamiltonian for quantum computation.
• Employing the Variational Quantum Eigensolver (VQE) to find the minimum eigenvalue (optimal solution).
• Experimenting with various ansatzes and optimization methods on simulators and real quantum devices.

Main Results:

• VQE performance is highly dependent on quantum hardware size and hyperparameter selection.
• Optimal hyperparameter choices enable VQE on real devices to reach solutions close to exact ones.
• The quantum algorithm demonstrates strong convergence towards classical solutions, even without error mitigation.
• Solution quality correlates with quantum processor dimension, as shown on different quantum devices.
• The study provides evidence for the best practices for VQE-based portfolio optimization.

Conclusions:

• The Variational Quantum Eigensolver (VQE) is a viable and efficient method for portfolio optimization on quantum computers.
• Careful selection of hyperparameters and sufficient quantum hardware are crucial for achieving high-quality results.
• Quantum computing, particularly VQE, holds promise for more efficient financial optimization as hardware scales.