SIAM Journal on Computing
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum cryptanalysis of hash and claw-free functions
ACM SIGACT News
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum Lower Bounds for the Collision and the Element Distinctness Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Complete Promise Problem for Statistical Zero-Knowledge
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Succinct quantum proofs for properties of finite groups
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Graph entropy and quantum sorting problems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum and classical query complexities of local search are polynomially related
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
The quantum query complexity of the hidden subgroup problem is polynomial
Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
Guest Column: NP-complete problems and physical reality
ACM SIGACT News
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the power of Ambainis lower bounds
Theoretical Computer Science
Quantum protocols for zero-knowledge systems
Quantum Information Processing
Quantum sampling for balanced allocations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The complexity of zero knowledge
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
The polynomial degree of recursive Fourier sampling
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Complexity classes of equivalence problems revisited
Information and Computation
How significant are the known collision and element distinctness quantum algorithms
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Physically-motivated dynamical algorithms for the graph isomorphism problem
Quantum Information & Computation
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Quantum money from hidden subspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Impossibility of succinct quantum proofs for collision-freeness
Quantum Information & Computation
The limits of quantum computers
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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(MATH) The collision problem is to decide whether a function X: { 1,&ldots;,n} → { 1, &ldots;,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Ω(n1/5) on the number of queries needed by a quantum computer to solve this problem with bounded error probability. The best known upper bound is O(n1/3), but obtaining any lower bound better than Ω(1) was an open problem since 1997. Our proof uses the polynomial method augmented by some new ideas. We also give a lower bound of Ω(n1/7) for the problem of deciding whether two sets are equal or disjoint on a constant fraction of elements. Finally we give implications of these results for quantum complexity theory.