Demonstration of topological data analysis on a quantum processor

Abstract

Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat. Commun. 7, 10138 (2016)] for calculating Betti numbers of data points -topological features that count the number of topological holes of various dimensions in a scatterplot. Here, we implement a proofof-principle demonstration of this quantum algorithm by employing a six-photon quantum processor to successfully analyze the topological features of Betti numbers of a network including three data points, providing new insights into data analysis in the era of quantum computing.

Proceedings of the 13th International Conference on Computational Semantics - Student Papers

“…TDA can be computationally expensive, as observed by many researchers, and also Huang et al (2018) to argue that quantum computing methods might be appropriate (if they materialize). However topological features seem to provide advantage when only small amount of the data is available, as shown here, and also in Doshi and Zadrozny (2018), who used only small percentage of data for preparation and training.…”

“…It is an open problem how exactly these new numerical features help entailment. Source of the figure:Huang et al (2018)…”

General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier

“…Our analytic complexity bounds also show that simulating a 8 × l circuit (l > 8) with depth (1 + 40 + 1), or a 10 × l (l > 10) circuit with depth (1 + 32 + 1) is within reach of current supercomputers.Quantum computers offer the promise of efficiently solving certain problems that are intractable for classical computers, most famously factorizing large numbers [1][2][3]. With the rapid progress of various quantum systems towards Noisy Intermediate-Scale Quantum computing devices [4][5][6][7][8][9][10][11], we are now on the verge of quantum supremacy [12], i.e. demonstrating that an actual quantum computer has the ability to do a computation that no classical computers can tackle, an important milestone in the field of computer science.…”

“…We point out here that although Eqs. (7,9) have higher time complexities compared to Eq. (5), they can be more conveniently parallelized when executed on a supercomputer because massive data transfer can be avoided.…”

“…In Fig.3(b) we show the space and time complexities computed from Eqs. (6)(7)(8)(9). To this end, we note that our algorithm can be straightforwardly combined with the fast sampling method in [24] to measure a large number of amplitudes.…”