Year: 2024
Type: article
Abstract: Extracting meaningful information from large data sets is a challenging computational task. Here we show that the problem of extracting the “shape” of classical data, formalized in the Clique Homology Problem, is QMA1-hard, i.e., at least as hard as quantum k-SAT. For inputs satisfying a suitable promise the problem is contained in QMA, the class of problems that can be efficiently verified by a quantum computer. These results are ultimately rooted in the assertion, first noted by Witten, that the study of homology is equivalent to the study of quantum ground states of supersymmetric systems, a class of physical systems exhibiting a symmetry relating bosonic and fermionic states. We anticipate that the results reported here will serve as the starting point for investigating the possibility of quantum advantage in computational topology and classical data analysis using techniques from quantum many-body physics.
Source: Nature Communications
Authors: Marcos Crichigno, Tamara Kohler
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $6,790
OpenAlex ID: W4404312875