More on quantum topological data analysis

 Two preprints on quantum topological data analysis (TDA) were posted to arXiv last week.

From the IBM team, Exponential advantage on noisy quantum computers. This is a follow-up to their proposal from last year, arXiv:2108.02811, implementing their linear depth NISQ-TDA algorithm (my earlier synopsis) using a trapped ion quantum processor. 

The introduction nicely frames the key ingredients required for demonstrating an end-to-end quantum advantage using near-term device, and then explains how NISQ-TDA meets all of the requirements, for example by having small input and output data sizes. Another advantage of NISQ-TDA is that the output observables, the Betti numbers, are known to be quantized topological invariants, leading to a robustness to shot noise and reducing the number of measurements required to obtain an accurate result. 

The article ends with the optimistic outlook that "a 96-qubit quantum computer with a two-qubit gate and measurement fidelity of ∼ 99.99% suffices to to achieve quantum advantage on the Betti number estimation problem." This really seems to me the strongest candidate for demonstrating a quantum advantage. Anyone interested in near-term quantum algorithms for machine learning applications should read this paper!

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A second preprint was posted by researchers from Deloitte, Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological Analysis. This work offers a more pessimistic viewpoint, stating that "the empirical results show the noise within the data is intensified with each encoding method as there is a clear change in the geometric structure of the original data, exhibiting information loss." However, their approach seems to be based on the original quantum TDA algorithm, based on Grover search and quantum phase estimation, which is not suited for near-term devices.