Quantum algorithm for persistent Betti numbers and topological data analysis

Understand

Topological data analysis (TDA) is an emergent field of data analysis.

• The critical step of TDA is computing the persistent Betti numbers.
• Existing classical algorithms for TDA are limited if we want to learn from high-dimensional topological features because the number of high-dimensional simplices grows exponentially in the size of the data.
• In the context of quantum computation, it has been previously shown that there exists an efficient quantum algorithm for estimating the Betti numbers even in high dimensions.