Variational Quantum Algorithms in Finance

Viktor Borysiuk, Olha R. Michuta

The article examines methods for applying quantum computing to solve optimization problems, which are critical in various fields such as logistics, finance, resource management, energy, and others. The potential of quantum algorithms, such as Grover's algorithm and Variational Quantum Algorithms (VQA), is explored for enhancing computational efficiency compared to classical methods. Quantum computing enables significant acceleration of optimal solution search processes and reduces the complexity of problems through parallel computing and quantum superposition.

Tatsuru Kikuchi

Hicham Benamer

Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.

RUBEN DAVID MAAREK

Pinaki Sen, Amandeep Singh Bhatia, Kamalpreet Singh Bhangu +1 more

In quantum computing, the variational quantum algorithms (VQAs) are well suited for finding optimal combinations of things in specific applications ranging from chemistry all the way to finance. The training of VQAs with gradient descent optimization algorithm has shown a good convergence. At an early stage, the simulation of variational quantum circuits on noisy intermediate-scale quantum (NISQ) devices suffers from noisy outputs. Just like classical deep learning, it also suffers from vanishing gradient problems. It is a realistic goal to study the topology of loss landscape, to visualize the curvature information and trainability of these circuits in the existence of vanishing gradients. In this paper, we calculate the Hessian and visualize the loss landscape of variational quantum classifiers at different points in parameter space. The curvature information of variational quantum classifiers (VQC) is interpreted and the loss function's convergence is shown. It helps us better understand the behavior of variational quantum circuits to tackle optimization problems efficiently. We investigated the variational quantum classifiers via Hessian on quantum computers, starting with a simple 4-bit parity problem to gain insight into the practical behavior of Hessian, then thoroughly analyzed the behavior of Hessian's eigenvalues on training the variational quantum classifier for the Diabetes dataset. Finally, we show how the adaptive Hessian learning rate can influence the convergence while training the variational circuits.

Marco Cerezo, Andrew Arrasmith, Ryan Babbush +8 more