Quantum Machine Learning qTDA for detecting financial crashes - Implementation Challenge!

[diyapandey3]

Research Paper We Plan To Implement:

Integral Betti signature confirms the hyperbolic geometry of brain, climate, and financial networks https://www.arxiv.org/pdf/2406.15505

Paper Summary/ Abstract:

This research paper delves into the application of topological data analysis (TDA) to discern the underlying geometric structures in complex datasets. As we know, higher dimensional datasets are important in many scientific domains- be it in economics, quantum or biology. By analyzing changes in Betti numbers, TDA can reveal shifts in underlying structures that precede these transitions. Further, the study of these curves effectively differentiates between Euclidean, spherical, and hyperbolic geometries within data matrices and serves beneficial for uncovering hidden strictures of data. In conclusion, it suggests that the findings reveal a hyperbolic character in datasets, something to look forward to for implementation.

Main Idea:

Several studies suggest that Betti numbers serve as effective indicators of market crashes. So, our main idea here is to do TDA of these available higher dimensional datasets for stock datasets and compare that later with the quantum topological data analysis.
Example: Detecting financial bubbles by using quantum topological data analysis (qTDA)

Proposed Technical Approach:

• Understanding the Algorithm:
  Quantum-Enhanced Topological Data Analysis: A Peep from an Implementation Perspective https://arxiv.org/pdf/2302.09553
  Quantum topological data analysis via the estimation of the density of states https://arxiv.org/abs/2312.07115
  Towards quantum advantage via topological data analysis https://doi.org/10.22331/q-2022-11-10-855

• Selection of Quantum Framework:
  We will be using Classiq and Qiskit for framework.

• Quantum Circuit Design:
  Once we load data and prepare point cloud we will be building Laplacian from it. here are several python package available for that, eg: GUDHI. The Betti number is the number of zero eigenvalues in the Laplacian .
  βk​=dim(ker(Δk​))
  After that, we plan to apply QPE for estimating the number of zero eigenvalues in the Laplacian matrix.

• Detecting Market Crashes: We will use the Lp norm to create pairwise distance curves for successive windows, and analyze those to see and predict where crashes is occurring.

• Simulation and Testing: We will compare our result and data to see how well it performs, circling back to the technical approach if it fails.

• Evaluation and Analysis: We also plan to uncover and see further applications of this as mentioned in the [paper beyond financial crashes as betti curves serves as a major source of dependency with these datasets.

• Scalability Considerations:
  QPE remains primarily theoretical. So, we will further discuss how the algorithm can be optimized for near-term and future quantum hardware.

Motivation for Implementation :

• Not only does a crash affect financial institutions, like commercial banks and the Federal Reserve, but it also affects the broader economy—driving increased inflation or altering a nation’s production of exports.

• Cross-Disciplinary Applications: Applying these techniques across diverse fields such as neuroscience, finance, and climate science can uncover universal patterns and principles governing complex systems.

Conclusion:

While their use in finance is still in its early stages, they show promise in various applications, such as credit risk prediction, fraud detection, financial bubble detection, capturing financial instability, etc.

This project is also an inspiration to us from a hackathon we recently participated. We will love to hear your feedbacks, resources and comments on how can we better approach this topic.
Thank you once again for the opportunity.

Regards:
Diya Pandey
Pritesh Thakur @Pritesh402
Sampada Wagle @unalivepeep
Yubraj Bhandari @yubrajbhandari923

[NadavClassiq]

It sounds like an ambitious and interesting project, @diyapandey3 !

We will be glad to have such a contribution in our repo!

Please note that we accept high-quality implementations in our repository and will be glad to accept a contribution that meets our standards. This

For which use will need to use Qiskit? As the classiq-library, we primarily accept contributions using Classiq.
Is there anything you will not be able to implement with Classiq?

Feel free to contact the community if you have any questions