2021/06/08 by John Kallaugher, Kallaugher, John · 2 citations
Computer Science · Physics and Astronomy · #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning and Algorithms #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques #cs.DS #quant-ph
paper · pdf · doi:10.48550/arxiv.2106.04633
openalex publication_date 2021/06/08 · arxiv created 2021/11/12 · arxiv updated 2021/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming algorithms can use asymptotically less space than their classical counterparts for certain problems. However, so far, all known examples of quantum advantages in streaming are for problems that are either specially constructed for that purpose, or require many streaming passes over the input. We give a one-pass quantum streaming algorithm for one of the best studied problems in classical graph streaming - the triangle counting problem. Almost-tight parametrized upper and lower bounds are known for this problem in the classical setting; our algorithm uses polynomially less space in certain regions of the parameter space, resolving a question posed by Jain and Nayak in 2014 on achieving quantum advantages for natural streaming problems.