Work

Basic quantum subroutines: finding multiple marked elements and summing numbers

Year: 2024

Type: article

Abstract: We show how to find all k marked elements in a list of size N using the optimal number O(Nk) of quantum queries and only a polylogarithmic overhead in the gate complexity, in the setting where one has a small quantum memory. Previous algorithms either incurred a factor k overhead in the gate complexity, or had an extra factor log⁡(k) in the query complexity.We then consider the problem of finding a multiplicative δ -approximation of s=∑i=1Nvi where v=(vi)∈[0,1]N , given quantum query access to a binary description of v . We give an algorithm that does so, with probability at least 1−ρ , using O(Nlog⁡(1/ρ)/δ) quantum queries (under mild assumptions on ρ ). This quadratically improves the dependence on 1/δ and log⁡(1/ρ) compared to a straightforward application of amplitude estimation. To obtain the improved log⁡(1/ρ) dependence we use the first result.

Source: Quantum

DOI: 10.22331/q-2024-03-14-1284

Authors: Joran van Apeldoorn, Sander Gribling, Harold Nieuwboer

Institutions: QuSoft, University of Amsterdam, Tilburg University, University of Copenhagen, Ruhr University Bochum

Language: Latvian

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: Villum Fonden, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, HORIZON EUROPE European Research Council