J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. J. Computer and System Sciences, 62:376--391, 2001. Home/Search Document Details and Download
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One Complexity Theorist's View of Quantum Computing - Fortnow (2000) (2 citations) (Correct)
....approximating the matrix entries would no longer keep us in the class. Space bounded classes also lack some of the robustness of BQP. For example if we do not allow a measurement until the end even simulating coin ips becomes dicult: we cannot reuse the coins and keep reversibility. See Watrous [29] for a discussion. 5 Using This Formulation Once you have the formulation of quantum machines described in Section 2, one immediately gets interesting results on quantum complexity. 8 Fortnow 5.1 AWPP Suppose we remove the unitary restriction in the de nition of BQP in Section 2. This yields ....
J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. In Proceedings of the 14th IEEE Conference on Computational Complexity, pages 180-187. IEEE Computer Society, Los Alamitos, 1999. 15
One-Dimensional Quantum Walks - Ambainis, Bach, Nayak, Vishwanath.. (3 citations) Self-citation (Watrous) (Correct)
....[4, 5] This gives another asymptotic form for the probability distribution. The SchrSdinger approach is also quite general and could be potentially applied to quantum walks on any Cayley graph. Related work Various quantum variants of random walks have previously been studied by a few authors [6, 12, 24, 32], but their results are, for the most part, unrelated to ours. The first study of quantum walks is apparently due to Meyer [24] Meyer s model (quantum lattice gas automata or QLGA) is equivalent to our two way infinite Hadamard walk, but he addresses different questions than the ones we ....
....[6] analyze quantum walks on trees and exhibit collections of graphs on which the quantum process hits one particular node exponentially faster than the corresponding classical process. The definition for quantum walks considered in these papers is completely different from ours. One of us [32] has considered unitary processes based on quantum walks on regular graphs in the context of spacebounded computation. In that paper the quantum processes considered are much different from those we study, as they were designed to suppress quantum effects (in order to closely approximate classical ....
J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. Journal of Computer and System Sciences, 62(2): 376-391, 2001.
One-Dimensional Quantum Walks - Ambainis, Bach, Nayak, Vishwanath.. (3 citations) Self-citation (Watrous) (Correct)
....[4, 5] This gives another asymptotic form for the probability distribution. The Schr odinger approach is also quite general and could be potentially applied to quantum walks on any Cayley graph. Related work Various quantum variants of random walks have previously been studied by a few authors [6, 12, 24, 32], but their results are, for the most part, unrelated to ours. The rst study of quantum walks is apparently due to Meyer [24] Meyer s model (quantum lattice gas automata or QLGA) is equivalent to our two way in nite Hadamard walk, but he addresses di erent questions than the ones we consider. ....
....Gutmann [6] analyze quantum walks on trees and exhibit collections of graphs on which the quantum process hits one particular node exponentially faster than the corresponding classical process. The de nition for quantum walks considered in these papers is completely di erent from ours. One of us [32] has considered unitary processes based on quantum walks on regular graphs in the context of spacebounded computation. In that paper the quantum processes considered are much di erent from those we study, as they were designed to suppress quantum e ects (in order to closely approximate classical ....
J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. Journal of Computer and System Sciences, 62(2): 376-391, 2001.
Quantum Random Walks and the Analysis of Discrete Quantum.. - Ambainis, Bach, Watrous (2000) Self-citation (Watrous) (Correct)
....paper. Farhi and Gutmann [4] analyze quantum random walks on trees and exhibit a collection of trees on which the quantum process hits one particular leaf exponentially faster than the corresponding classical process. Their model, results, and methods seem to be quite di erent from ours. Watrous [15] considered quantum processes on graphs that mimic classical random walks in order to obtain results about space bounded quantum computation. In this case, however, the quantum 2 processes are designed so that quantum e ects do not ruin the behavior given by classical random walks on graphs, and ....
J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. In Proceedings of the 14th Annual IEEE Conference on Computational Complexity, pages 180-187, 1999.
Exponential Algorithmic Speedup by a Quantum Walk - Andrew Childs Richard (Correct)
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J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. J. Computer and System Sciences, 62:376--391, 2001.
One Complexity Theorist's View of Quantum Computing - Lance Fortnow Nec (2000) (2 citations) (Correct)
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J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. Journal of Computer and System Sciences, 62(2):376-391, 2001. 13
Exponential Algorithmic Speedup by a Quantum Walk - Childs, Cleve, Deotto.. (2 citations) (Correct)
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J. Watrous. Quantum simulations of classical random walks and undirected graph connectivity. J. Computer and System Sciences, 62:376--391, 2001.
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