Fisher information and quantum potential well model for finance

Hongbing Su

Amandeep Singh Bhatia, Sabre Kais

Federated Learning (FL) has become increasingly popular across different sectors, offering a way for clients to work together to train a global model without sharing sensitive data. It involves multiple rounds of communication between the global model and participating clients, which introduces several challenges like high communication costs, heterogeneous client data, prolonged processing times, and increased vulnerability to privacy threats. In recent years, the convergence of federated learning and parameterized quantum circuits has sparked significant research interest, with promising implications for fields such as healthcare and finance. By enabling decentralized training of quantum models, it allows clients or institutions to collaboratively enhance model performance and outcomes while preserving data privacy. Recognizing that Fisher information can quantify the amount of information that a quantum state carries under parameter changes, thereby providing insight into its geometric and statistical properties. We intend to leverage this property to address the aforementioned challenges. In this work, we propose a Quantum Federated Learning (QFL) algorithm that makes use of the Fisher information computed on local client models, with data distributed across heterogeneous partitions. This approach identifies the critical parameters that significantly influence the quantum model's performance, ensuring they are preserved during the aggregation process. Our research assessed the effectiveness and feasibility of QFL by comparing its performance against other variants, and exploring the benefits of incorporating Fisher information in QFL settings. Experimental results on ADNI and MNIST datasets demonstrate the effectiveness of our approach in achieving better performance and robustness against the quantum federated averaging method.

Cecilia N. Isonguyo, K. J. Oyewumi, Opeyemi S. Oyun +1 more

The Heisenberg uncertainty relation as well as the Fisher information are presented analytically and numerically for the Generalized radial Yukawa potential. The probability density for the ground and first excited state has been analyzed via the Fisher information for this potential model. Some numerical results are obtained. From the numerical results obtained, we observed that, for n = 0, 1, the position-space Fisher information Ir increases with increasing potential parameter a, while the momentum-space Fisher information Iρ initially increases, and later decreases with increasing potential parameter a. The Fisher-information-based uncertainty relation and the Heisenberg uncertainty relation have been verified to hold for this atomic model. In addition, we observed a squeezed phenomenon in some of the results in position r and momentum ρ for the ground and first excited states.

Hongbing Su

C. A. Onate, I. B. Okon, E. Omugbe +4 more

The solutions of two potentials with one potential made up of a combination of constant, Yukawa, and inversely quadratic potentials and the other made up of constant, Coulomb, and inversely quadratic potentials are obtained under the radial Schrödinger equation using the elegant parametric Nikiforov–Uvarov method. The energy equations and their corresponding wave functions are obtained in a close and compact form. The Fisher information for configuration space and momentum space are obtained for each combination of the potentials. It has been revealed that the energy eigenvalues of each combined potential model has a turning point. It is also shown that one special case in one combined potentials and another special case in the other combined potentials have equivalent energy eigenvalues. The results for the constant potential as a subset potential in each combination are not exactly the same. The Fisher information for each combined potentials and their respective subset potentials satisfied Fisher information-based uncertainty relation. It is also shown that the effect of the screening parameter on the Fisher information at the ground state and at the first excited state for one of the combining potential has a diffused format.

Paolo Gibilisco, Tommaso Isola