Finding the Optimal Currency Composition of Foreign Exchange Reserves with a Quantum Computer

Paper: arXiv 2303.01909

Authors: Martin Vesely

Abstract

Portfolio optimization is an inseparable part of strategic asset allocation at the Czech National Bank. Quantum computing is a new technology offering algorithms for that problem. The capabilities and limitations of quantum computers with regard to portfolio optimization should therefore be investigated. In this paper, we focus on applications of quantum algorithms to dynamic portfolio optimization based on the Markowitz model. In particular, we compare algorithms for universal gate-based quantum computers (the QAOA, the VQE and Grover adaptive search), single-purpose quantum annealers, the classical exact branch and bound solver and classical heuristic algorithms (simulated annealing and genetic optimization). To run the quantum algorithms we use the IBM Quantum\textsuperscript{TM} gate-based quantum computer. We also employ the quantum annealer offered by D-Wave. We demonstrate portfolio optimization on finding the optimal currency composition of the CNB’s FX reserves. A secondary goal of the paper is to provide staff of central banks and other financial market regulators with literature on quantum optimization algorithms, because financial firms are active in finding possible applications of quantum computing.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a practical and novel application of quantum algorithms (QAOA, VQE, D-Wave annealing) to a real-world central bank reserve allocation problem. While relying on standard portfolio optimization formulations, the cross-architecture quantum benchmarking provides strong technical value and useful empirical comparisons against classical solvers.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Quantum vs Classical Algorithms for Dynamic FX Reserve Optimization] --> B[Data Inputs: CNB Foreign Exchange Reserve Data & Markowitz Model]
    
    B --> C[Algorithm Comparison & Execution]
    
    subgraph C [Computational Processes]
        C1[Quantum Approaches: Gate-based IBM QAOA, VQE, GAS & D-Wave Annealer]
        C2[Classical Approaches: Exact Branch & Bound, Simulated Annealing, Genetic Algo]
    end
    
    C --> D[Performance & Feasibility Analysis]
    
    D --> E[Key Outcomes: Benchmarked Quantum Limitations/Capabilities & Provided Central Bank Guidance]