Quantum Random Walks – New Method for Designing Quantum Algorithms

DOI10.1007/978-3-540-77566-9_1zbMath1132.68382OpenAlexW1566596544MaRDI QIDQ5448636

Andris Ambainis

Publication date: 7 March 2008

Published in: SOFSEM 2008: Theory and Practice of Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-77566-9_1

Mathematics Subject Classification ID

Quantum computation (81P68) Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) (68T20) General topics in the theory of algorithms (68W01)

Related Items (6)

Quantum walk and its application domains: a systematic review ⋮ Probability distributions for Markov chain based quantum walks ⋮ Open quantum random walks ⋮ Evolutionary algorithms for quantum computers ⋮ Discrete-time quantum walk on the Cayley graph of the dihedral group ⋮ Quantum walks: a comprehensive review

Cites Work

• A lower bound on the quantum query complexity of read-once functions
• Quantum complexity of testing group commutativity
• The quantum query complexity of approximating the median and related statistics
• Any AND-OR Formula of Size N Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Spatial search and the Dirac equation
• Quantum lower bounds for the collision and the element distinctness problems
• Exponential algorithmic speedup by a quantum walk
• Quantum verification of matrix products
• QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
• Quantum Algorithms for the Triangle Problem
• Quantum cryptanalysis of hash and claw-free functions
• Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
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