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Exponential Algorithmic Speedup by a Quantum Walk  (Make Corrections)  (2 citations)
Andrew M. Childs Richard Cleve + Enrico Deotto Edward Farhi Sam Gutmann...



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Abstract: We construct a black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a di#erent technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk e#ciently in our black box setting. We then show how this quantum walk solves our problem by rapidly traversing a graph. Finally, we prove... (Update)

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BibTeX entry:   (Update)

@misc{ richard-exponential,
  author = "Andrew Childs Richard",
  title = "Exponential Algorithmic Speedup by a Quantum Walk",
  url = "citeseer.ist.psu.edu/764058.html" }
Citations (may not include all citations):
1120   Handbook of Mathematical Functions (context) - Abramowitz, Stegun - 1972
173   Quantum complexity theory - Bernstein, Vazirani - 1997  ACM   DBLP
168   Algorithms for quantum computation: discrete logarithms and .. - Shor - 1997  DBLP
167   Quantum Computation and Quantum Information (context) - Nielsen, Chuang - 2000  ACM
144   the power of quantum computation - Simon - 1997
126   Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1992  ACM
84   an estimate of the chromatic class of a p-graph (context) - Vizing - 1964
40   Quantum measurements and the abelian stabilizer problem (context) - Kitaev  DBLP
23   The hidden subgroup problem and eigenvalue estimation on a q.. - Mosca, Ekert - 1999  ACM   DBLP
22   From quantum cellular automata to quantum lattice gasses - Meyer - 1996
20   Polynomial-time quantum algorithms for Pell's equation and t.. - Hallgren - 2002  ACM   DBLP
18   Normal subgroup reconstruction and quantum computation using.. - Hallgren, Russell et al. - 2000  ACM   DBLP
16   Quantum mechanical algorithms for the nonabelian hidden subg.. - Grigni, Schulman et al. - 2001  ACM   DBLP
14   Universal quantum simulators (context) - Lloyd - 1996
9   and the universal quantum computer (context) - Deutsch, the - 1985
7   Quantum walks on graphs - Aharonov, Ambainis et al. - 2001  ACM   DBLP
7   Adiabatic quantum state generation and statistical zero know.. - Aharonov, Ta-Shma - 2003  ACM   DBLP
7   Quantum simulations of classical random walks and undirected.. - Watrous - 2001  ACM   DBLP
7   Quantum computation and decision trees (context) - Farhi, Gutmann - 1998
6   Quantum algorithms for solvable groups - Watrous - 2001  ACM   DBLP
5   cient quantum algorithms for shifted quadratic character pro.. (context) - van Dam, Hallgren
5   erence between quantum and classical random walks (context) - Childs, Farhi et al. - 2002
4   classical query complexity separations (context) - de Beaudrap, Cleve et al. - 2002
4   One-dimensional quantum walks - Ambainis, Bach et al. - 2001  ACM   DBLP
3   cient quantum algorithms for estimating Gauss sums (context) - van Dam, Seroussi
2   cient quantum algorithms for some instances of the non-abeli.. (context) - Ivanos, Magniez et al.
2   Quantum walks on the hypercube - Moore, Russell - 2002  ACM   DBLP
2   Quantum random walks hit exponentially faster (context) - Kempe
2   Personal communication (context) - Goldstone - 2002

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