Kohei Oshio

Quantum topological data analysis is one of the most promising areas for quantum advantage. In particular, the LGZ algorithm is the most basic algorithm for estimating Betti numbers, which are considered to be the essential shape of point clouds. Since LGZ, various quantum algorithms have been proposed, but many of them are based on FTQC and require a large number of quantum resources. In this paper, we propose a QTDA algorithm that does not require ancilla bits using a Hamiltonian based on supersymmetry, which has not been widely used in existing research. In particular, by imposing constraints on the graph, we show that there is always a known 0 eigenvalue and eigenstate in the Hamiltonian, this allows us to use ancilla-free measurement algorithms. Moreover, by using randomization, we reduce the required number of samples.