One-dimensional quantum walks

By Andris Ambainis, E. Bach, Ashwin Nayak, Ashvin Vishwanath, John Watrous. Symposium on the Theory of Computing, 2001

628 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/81b76bfe5a55dc98055c2dd0602d451d882013c1

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Citations in the corpus

Quantum walks: a comprehensive review (2012, methodology): “Following [31,339], a quantum walk on an infinite line after t steps can be written as |ψ〉t = Û t |ψ〉initial [Eq.”
Quantum random walks: An introductory overview (2003, background): “All along the way we will outline open questions and future directions.”
On the Relationship Between Continuous- and Discrete-Time Quantum Walk (2008, methodology): “As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model.”
A new type of limit theorems for the one-dimensional quantum random walk (2002, background): “[1], they gave two general ideas for analyzing quantum random walks.”
Exponential algorithmic speedup by a quantum walk (2002, methodology): “In the present paper, we modify the example presented in [7] and construct a black box problem based on it that can be solved e.ciently a quantum algorithm that simulates a quantum walk, whereas no classical algorithm can solve the problem in subexponential time.”
Quantum Walk Based Search Algorithms (2008, background): “by Watrous in his works related to space bounded computations [37]. Diﬀerent parameters related to quantum walks and possible speedups of classical algorithms were investigated by several researchers [30,8,3,29,19,32]. The potential of discrete time quantum walks with respect to searching problems w”
Search via quantum walk (2006, background): “Afterwards notions related to quantum walks, such as mixing time, and deviation from starting state, were studied for restricted graphs by several researchers [22, 7, 3, 23], suggesting the possibility of speedup of classical algorithms based on random walk.”
Quantum walk algorithm for element distinctness (2003, methodology): “r ﬂavor but uses completely diﬀerent methods to search the graph (quantum walk instead of ‘’divide-and-conquer”). Quantum walks. There has been considerable amount of research on quantum walks (e.g., [5, 30, 4, 9]) and their applications (e.g., [20, 18, 26, 31, 21]). We refer to [27] for an excellen”
Analytic Combinatorics in Several Variables (2013, background): “This gives us all we need in order to compute; for more on the interpretation of quantum walks see Ambainis et al. (2001); Baryshnikov, Brady, et al.”
Quantum walks in higher dimensions (2001, methodology): “Quantum physics introduces new perspectives, such as quantum diffusion [1], quantum stochastics [2], and quantum walks [3, 4, 5, 6].”