Tad Hogg  Home/Search
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Abstract: We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows... (Update)
Context of citations to this paper: More
...for solving Sat problem. For example, Hogg has proposed a simple quantum algorithm for satisfiability and constraint satisfaction problems [46]. He has observed similar phase transition on random 3 Sat problems as seen in classical computational methods. Finally, Lipton has...
.... Grover s search algorithm can be used to speed up combinatorial search within a domain of size N to a time bound of O( p N ) Hogg [Hog96] Hogg, Yanik [HY98] investigate similar quantum search techniques for local and other combinatorial search problems) and in this case...
Cited by: More
A Framework for Quantum Search Heuristics - Hogg (1996) (Correct)
Finding Solutions to NP Problems: Philosophical Differences.. - Greenwood (2001) (Correct)
Quantum Computation Primitives - Frank (1996) (Correct)
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0.5: The Scaling of Search Cost - Gent, MacIntyre, Prosser, Walsh (1997) (Correct)
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BibTeX entry: (Update)
T. Hogg, Quantum Computing and Phase Transitions in Combinatorial Search, (Online preprint quant-ph/9508012), J. of Artificial Intelligence Research 4,91-128 (1996). http://citeseer.ist.psu.edu/hogg96quantum.html More
@article{ hogg96quantum,
author = "Tad Hogg",
title = "Quantum Computing and Phase Transitions in Combinatorial Search",
journal = "Journal of Artificial Intelligence Research",
volume = "4",
pages = "91-128",
year = "1996",
url = "citeseer.ist.psu.edu/hogg96quantum.html" }
Citations (may not include all citations):744 Matrix Computations (context) - Golub, Loan - 1983
686 A Guide to the Theory of NP-Completeness (context) - Garey, Johnson - 1979
320 Hard and easy distributions of SAT problems - Mitchell, Selman et al. - 1992 DBLP
210 Minimizing conflicts: A heuristic repair method for constrai.. - Minton, Johnston et al. - 1992 DBLP
186 Constraint satisfaction (context) - Mackworth - 1992 ACM
173 Quantum complexity theory - --, Vazirani - 1993 ACM DBLP
168 Algorithms for quantum computation: Discrete logarithms and .. - Shor - 1994 DBLP
148 A First Course in Stochastic Processes (context) - Karlin, Taylor - 1975
132 Randomized Algorithms (context) - Motwani, Raghavan - 1995 ACM DBLP
81 The Principles of Quantum Mechanics (context) - Dirac - 1958
76 Exploiting the deep structure of constraint problems (context) - Williams, Hogg - 1994 ACM DBLP
70 Quantum computational networks (context) - Deutsch - 1989
68 An empirical study of phase transitions in binary constraint.. (context) - Prosser - 1996 DBLP
62 The hardest constraint problems: A double phase transition (context) - Hogg, Williams - 1994 DBLP
59 Locating the phase transition in binary constraint satisfact.. - Smith, Dyer - 1996 DBLP
46 Quantum computations with cold trapped ions (context) - Cirac, Zoller - 1995
41 Experimental results on the cross-over point in satisfiabili.. (context) - Crawford, Auton - 1993
34 Quantum mechanical hamiltonian models of Turing machines (context) - Benioff - 1982
31 Phase transitions and the search problem (context) - Hogg, Huberman et al. - 1996 ACM DBLP
24 Information is physical (context) - -- - 1991
23 Maintaining coherence in quantum computers (context) - Unruh - 1995
22 Refining the phase transitions in combinatorial search (context) - Hogg - 1996
21 Parallel quantum computation - Margolus - 1990
18 Quantum computation (context) - DiVincenzo - 1995 ACM
17 Quantum theory (context) - Deutsch - 1985
15 Quantum-mechanical computers (context) - Lloyd - 1995
13 Is quantum mechanically coherent computation useful (context) - Landauer - 1994
11 Implicates and prime implicates in random 3-SAT (context) - Schrag, Crawford - 1996 DBLP
11 Epsilon-transformation: Exploiting phase transitions to solv.. - Pemberton, Zhang - 1996 DBLP
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7 Quantum computers (context) - Chuang, Laflamme et al. - 1995 ACM
6 Shor's quantum algorithm for factorising numbers (context) - Ekert, Jozsa - 1995
6 The stabilization of quantum computations (context) - Berthiaume, Deutsch et al. - 1994
4 Results on two-bit gate design for quantum computers - DiVincenzo, Smolin - 1994
3 Phase transitions in constraint satisfaction search (context) - Hogg - 1994
3 Quantum cryptography: Uncertainty in the service of privacy - -- - 1992
2 Coherent laser control of the product distribution obtained .. (context) - Zhu, Kleiman et al. - 1995
2 of the 35th Symposium on Foundations of Computer Science (context) - Goldwasser, Ed - 1995
2 A new method for solving hard satisfiability problems (context) - Intelligence, Selman et al. - 1992 DBLP
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1 Optimization by simulated annealing (context) - Computing, in et al. - 1983 ACM
1 Mathematica: A System for Doing Mathematics by Computer (context) - Intelligence, Wolfram - 1991 ACM
1 A strategy for the chemical synthesis of nanostructures (context) - Muller, Klein et al. - 1995
1 Quantum mechanical computers (context) - Phys, Feynman - 1986
1 A potentially realizable quantum computer (context) - Press - 1993
1 Atomic-scale desorption through electronic and vibrational e.. (context) - Shen, Wang et al. - 1995
1 The TSP phase transition (context) - Freeman, Francisco et al. - 1995 ACM DBLP
1 Partial constraint satisfaction (context) - NJ, Wallace - 1992 ACM DBLP
1 Computation and quantum superposition (context) - Jozsa - 1992 ACM
1 A unified view of complexity transitions on the travelling s.. (context) - Zhang, Korf - 1996
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