Hybrid quantum-classical optimization for financial index tracking

Abstract

Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a challenging NP-hard problem even for moderately large indices consisting of dozens or hundreds of assets, thereby requiring heuristic methods to find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as a plausible method to improve performance of current schemes. In this work we introduce a heuristic pruning algorithm to find weighted combinations of assets subject to cardinality constraints. We further consider different strategies to respect such constraints and compare the performance of relevant quantum ansätze and classical optimizers through numerical simulations.

arXiv comment24 pages, 12 figures. A few changes in structure implemented in version 2

References in corpus (20)

• Quantum Computing in the NISQ era and beyond
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Quantum computing for finance: overview and prospects
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum Risk Analysis
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Improving Variational Quantum Optimization using CVaR
• Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
• Performance of hybrid quantum/classical variational heuristics for combinatorial optimization
• A direct formulation for sparse PCA using semidefinite programming
• Forecasting financial crashes with quantum computing
• Training a Binary Classifier with the Quantum Adiabatic Algorithm
• Quantum computational finance: quantum algorithm for portfolio optimization
• Hybrid quantum-classical optimization for financial index tracking
• A Risk Ratio Comparison of $l_0$ and $l_1$ Penalized Regression
• Portfolio rebalancing experiments using the Quantum Alternating Operator Ansatz
• Cardinality constrained portfolio selection via factor models

Cited by in corpus (7)

• Quantum computing for finance
• Filtering variational quantum algorithms for combinatorial optimization
• Quantum variational optimization: The role of entanglement and problem hardness
• Hybrid quantum-classical optimization for financial index tracking
• Approaches to Constrained Quantum Approximate Optimization
• A systematic literature review on solution approaches for the index tracking problem in the last decade
• Demonstration of Hardware Efficient Photonic Variational Quantum Algorithm