QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS

2003/12/01 by Andris Ambainis, ANDRIS AMBAINIS · 11 citations
Computer Science · #Computer science #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Quantum-Dot Cellular Automata #Statistical physics #Theoretical computer science

paper · doi:10.1142/s0219749903000383

crossref issued 2003/12/01 · crossref published 2003/12/01 · crossref published-print 2003/12/01 · openalex publication_date 2003/12/01 · crossref created 2004/02/06 · crossref published-online 2012/01/25 · crossref deposited 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01 · crossref indexed 2026/08/06

Abstract

Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.

Citations

• Quantum Computation and Decision Trees
• Strengths and Weaknesses of Quantum Computing
• QUANTUM WALKS ON GENERAL GRAPHS
• Exponential algorithmic speedup by a quantum walk
• Spatial search by quantum walk
• A fast quantum mechanical algorithm for database search

Cited by

• Quantumness of noisy quantum walks: A comparison between measurement-induced disturbance and quantum discord
• Spectral mapping theorem of an abstract quantum walk
• Quantum Complexity Bounds for Independent Set Problems
• Quantum search with interacting Bose-Einstein condensates
• Limits of quantum speedup in photosynthetic light harvesting
• Relativistic effects in quantum walks: Klein's paradox and zitterbewegung
• Weak limit of the three-state quantum walk on the line
• Connection between continuous and discrete time quantum walks. From D-dimensional lattices to general graphs
• Parrondoʼs game using a discrete-time quantum walk
• On the Convergence of Markov Chain Distribution within Quantum Walk Circuit Subspace
• Causality, localization, and universality of monitored quantum walks with long-range hopping