Lämminkäynnistystekniikat rahoituksen portfolio optimointi ongelman ratkaisemiseksi VQE algoritmilla
Julia Ripatti
A portfolio optimization problem is highly important for the financial sector and critical in portfolio management. To solve the mean-variance portfolio optimization classically, the time resources needed grow exponentially with the number of stocks used. In practice, the mean-variance portfolio optimization can be solved for a few hundred assets with classical computers. Due to the exponential nature of the portfolio optimization problem, quantum computing can be utilized to improve the computation process. For solving the portfolio optimization with quantum computers we use hybrid algorithms, build of quantum and classical computing parts. More specifically, we consider the most promising hybrid algorithm, called Variational Quantum Eigensolver (VQE), which is particularly suitable for near-term quantum hardware. To maximize the potential of the near-term quantum computers, we aim to discover the suitable form of the most crucial components of the VQE algorithm. In addition to this, to further improve the performance of the VQE algorithm, we investigate the utilization of various warm-start techniques for maximizing the efficient use of the limited quantum resources. The crucial components of the VQE algorithm are the quantum circuit, i.e. ansatz, and classical optimizer. We approach the problem of finding the suitable ansatz for portfolio optimization from two different directions, with theoretical and hardware-efficient approaches. We start with the theoretically best possible, but complex structured chemistry-inspired ansatz and continue to study the capabilities of hardware efficient, but ad hoc, Dicke state ansatzes. For optimizing the classical component of the VQE algorithm, we will briefly consider the effect of various classical optimizers on the performance of the most suitable ansatzes. When the most promising components of the VQE algorithm are known, the application of various warm-start techniques of parameter initialization can begin. In initialization strategies, we investigate how the special features of Dicke state ansatzes can be used to develop tailored initialization strategies. We also investigate how optimal parameters of related problems can be utilized in parameter initialization. Our results draw clear differences in warm-startability between various ansatzes and optimizers. The results on the warm-startability of different ansatzes are important for the quantum algorithm design, because often when solving especially real-world optimization problems, the original problem can change just a little, and therefore warm-start techniques can be highly beneficial. Based on the results the Dicke state ansatzes can be surprisingly useful and their special features allow us to develop a successful initialization strategy.
Työväentutkimus Vuosikirja•Dec 19, 2024•0 citations