Work

Quantum Time–Space Tradeoff for Finding Multiple Collision Pairs

Year: 2023

Type: article

Abstract: We study the problem of finding K collision pairs in a random function f : [N] → [N] by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase significantly when the size of the available memory is limited. Namely, we demonstrate that any algorithm using S qubits of memory must perform a number T of queries that satisfies the tradeoff T 3 S ≥ Ω (K 3 N) . Classically, the same question has only been settled recently by Dinur [ 22 ], who showed that the Parallel Collision Search algorithm of van Oorschot and Wiener [ 36 ] achieves the optimal time–space tradeoff of T 2 S = Θ (K 2 N) . Our result limits the extent to which quantum computing may decrease this tradeoff. Our method is based on a novel application of Zhandry’s recording query technique [ 42 ] for proving lower bounds in the exponentially small success probability regime. As a second application, we give a simpler proof of the time–space tradeoff T 2 S ≥ Ω (N 3 ) for sorting N numbers on a quantum computer, which was first obtained by Klauck, Špalek, and de Wolf [ 30 ].

Source: ACM Transactions on Computation Theory

DOI: 10.1145/3589986

Authors: Yassine Hamoudi, Frédéric Magniez

Institutions: Simons Foundation, Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Recherche en Informatique Fondamentale

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funders: U.S. Department of Energy, Agence Nationale de la Recherche, QuantERA, Simons Institute for the Theory of Computing, University of California Berkeley