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Abstract: We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a superposition of inputs. If the algorithm works correctly, its state becomes entangled with the superposition over inputs. We bound the number of queries needed to achieve a sufficient entanglement and this implies a lower bound on the number of queries for the... (Update)
Context of citations to this paper: More
.... Background Most of what is known about the power of quantum computing can be cast in the query or decision tree model [1, 2, 3, 5, 6, 9, 10, 11, 18, 22, 23]. Here one counts only the number of queries to the input, not the number of computational steps. The appeal of this...
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BibTeX entry: (Update)
A. Ambainis. Quantum lower bounds by quantum arguments. quantph /0002066. http://citeseer.ist.psu.edu/article/ambainis00quantum.html More
@inproceedings{ ambainis00quantum,
author = "Andris Ambainis",
title = "Quantum lower bounds by quantum arguments",
pages = "636--643",
year = "2000",
url = "citeseer.ist.psu.edu/article/ambainis00quantum.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996 ACM DBLP
164 Polynomial time algorithms for prime factorization and discr.. - Shor - 1997
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997 ACM DBLP
57 The probabilistic communication complexity of set intersecti.. (context) - Kalyanasundaram, Schnitger - 1987
50 the distributional complexity of disjointness (context) - Razborov - 1992
49 Quantum lower bounds by polynomials - Beals, Buhrman et al. ACM DBLP
25 Quantum measurements and the Abelian stabilizer problem - Yu DBLP
23 Philosophical Transactions of the Royal Society of London (context) - Vazirani, power et al. - 1998
22 Quantum communication complexity of sampling - Ambainis, Schulman et al.
19 Communication complexity lower bounds by polynomials - Buhrman, de Wolf ACM DBLP
16 Bounds for small-error and zero-error quantum algorithms - Buhrman, Cleve et al.
15 Quantum algorithm for the collision problem - Brassard, Hyer et al. - 1997
15 The quantum query complexity of approximating the median and.. - Nayak, Wu - 1999 ACM DBLP
6 How fast can a quantum computer search (context) - Grover
6 classical communication and computation (context) - Buhrman, Cleve et al.
5 A better lower bound for quantum algorithms searching an ord.. (context) - Ambainis ACM DBLP
5 Lower bounds of quantum black-box complexity and degree of a.. (context) - Shi
1 Also STOC'89 (context) - Nisan, decision et al. - 1991
The graph only includes citing articles where the year of publication is known.
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