Portfolio Optimization of 40 Stocks Using the DWave Quantum Annealer (2007.01430v1)

Abstract: We investigate the use of quantum computers for building a portfolio out of a universe of U.S. listed, liquid equities that contains an optimal set of stocks. Starting from historical market data, we look at various problem formulations on the D-Wave Systems Inc. D-Wave 2000Q(TM) System (hereafter called DWave) to find the optimal risk vs return portfolio; an optimized portfolio based on the Markowitz formulation and the Sharpe ratio, a simplified Chicago Quantum Ratio (CQR), then a new Chicago Quantum Net Score (CQNS). We approach this first classically, then by our new method on DWave. Our results show that practitioners can use a DWave to select attractive portfolios out of 40 U.S. liquid equities.

• The paper investigates using the D-Wave 2000Q quantum annealer for optimizing financial portfolios by formulating the problem as a QUBO compatible with quantum annealing.
• Results show the quantum annealer produces competitive solutions on the efficient frontier, albeit tending towards conservative risk levels compared to some classical algorithms.
• The research suggests quantum solutions can potentially improve classical optimization methods as hybrid seeds and highlights the feasibility of quantum computing for large-scale financial optimization.

Portfolio Optimization of 40 Stocks Using DWave's Quantum Annealer

The paper "Portfolio Optimization of 40 Stocks Using DWave's Quantum Annealer" investigates the application of quantum computing to the classical problem of financial portfolio optimization. The work leverages the D-Wave Systems Inc. D-Wave 2000Q™ quantum annealer to address the portfolio selection challenge, emphasizing the goal of maximizing returns while minimizing risk.

Overview and Methodology

The key focus of this research is on developing and comparing different optimization strategies for selecting an optimal portfolio from a set of 40 U.S. listed equities. Initially, the authors approach the problem using classical methods, particularly focusing on the Sharpe Ratio and the so-called Chicago Quantum Ratio (CQR). However, they also introduce a novel metric named the Chicago Quantum Net Score (CQNS), better suited for optimization using a quantum annealer due to its formulation as a Quadratic Unconstrained Binary Optimization (QUBO) problem.

Classical methods such as brute force, genetic algorithms, random sampling, heuristic approaches, and simulated annealing serve as benchmarks to evaluate the performance of the DWave system. The paper details the transformation of classical metrics into forms compatible with the Ising model of quantum annealing, a process required to implement the optimization on DWave's architecture.

Implementation on Quantum Hardware

The authors extensively describe the translation of the portfolio optimization problem into a suitable format for DWave's quantum annealer. They discuss the use and tuning of different parameters such as chain strength and qubit scaling to efficiently resolve the computational challenge while ensuring the robustness of the solutions provided by the quantum system. The paper's approach demonstrates a practical application of quantum annealing in finance, addressing issues such as the embedding of problem instances onto the quantum processing hardware.

Results and Comparative Analysis

The results obtained from the quantum annealer are compared against classical algorithms. The paper shows that DWave's solutions generally reach a favorable position on the efficient frontier, indicating competitive performance in balancing risk and return. However, the quantum solutions tend toward conservative risk levels when compared with random sampling and genetic algorithms.

From a computational perspective, the quantum annealer effectively explores the solution space of $2^{40}$ possibilities, showcasing its potential in solving combinatorially complex problems where classical algorithms falter due to constraints in memory and processing power.

Theoretical and Practical Implications

This research underscores the feasibility and growing relevance of quantum computing in addressing large-scale optimization problems within finance. It highlights the importance of formulation adjustments to capitalize on quantum annealing capabilities, specifically when transitioning from traditional metrics to those computable by such devices.

One of the pivotal outcomes of the research is the potential operational advantage of quantum methods akin to hybrid approaches. The authors suggest that quantum solutions can serve as valuable input (seeds) for refining classical optimization methods, such as genetic algorithms, thereby improving the quality and speed of results.

Future Directions

The paper concludes with recommendations for future research, emphasizing the need to test alternative forms of quantum optimization, such as reverse annealing and hybrid solvers, and the desire to include more diversified assets beyond equities, like bonds and commodities. These future efforts are anticipated to advance the adaptability and efficiency of quantum annealers in portfolio management and potentially broaden their impact across various financial instrument types.

Overall, the work provides an insightful exploration into the promising intersection of quantum computing and financial portfolio optimization, bridging classical finance theories and modern computational techniques.