Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Dense quantum coding and a lower bound for 1-way quantum automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
An introduction to quantum computing for non-physicists
ACM Computing Surveys (CSUR)
Counting by quantum eigenvalue estimation
Theoretical Computer Science
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computational complexity of uniform quantum circuit families and quantum Turing machines
Theoretical Computer Science
Quantum computing – Facts and folklore
Natural Computing: an international journal
Minds and Machines
Quantum Algorithms for Highly Structured Search Problems
Quantum Information Processing
Why haven't more quantum algorithms been found?
Journal of the ACM (JACM)
Quantum Search Algorithms in Science and Engineering
Computing in Science and Engineering
IEEE Intelligent Systems
Computing with quanta-impacts of quantum theory on computation
Theoretical Computer Science - Natural computing
Quantum communication and complexity
Theoretical Computer Science - Natural computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fourier transforms and quantum computation
Theoretical aspects of computer science
A Foundation of Programming a Multi-tape Quantum Turing Machine
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Quantum Database Search by a Single Query
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Search on Structured Problems
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Entanglement and the Communication Complexity of the Inner Product Function
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Computer Can Not Speed Up Iterated Applications of a Black Box
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Separating Quantum and Classical Learning
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Quantum Multi-prover Interactive Proof Systems with Limited Prior Entanglement
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Average-Case Quantum Query Complexity
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
On Quantum Computation with Some Restricted Amplitudes
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Quantum Public-Key Cryptosystems
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Analysis of Quantum Functions (Preliminary Version)
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Fourier Transforms and Quantum Computation
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
Qubit Logic, Algebra and Geometry
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Introduction to Recent Quantum Algorithms
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
One complexity theorist's view of quantum computing
Theoretical Computer Science - Algorithms,automata, complexity and games
Mathematical models of quantum computation
New Generation Computing
Graph coloring with quantum heuristics
Eighteenth national conference on Artificial intelligence
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Quantum time-space tradeoffs for sorting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Information and Computation
A Better Lower Bound for Quantum Algorithms Searching an Ordered List
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum multi-prover interactive proof systems with limited prior entanglement
Journal of Computer and System Sciences
On the simulation of quantum Turing machines
Theoretical Computer Science
ACM SIGACT News
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)
A Stochastic Limit Approach to the SAT Problem
Open Systems & Information Dynamics
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
Progress in Quantum Algorithms
Quantum Information Processing
Guest Column: NP-complete problems and physical reality
ACM SIGACT News
Computing in Science and Engineering
Is partial quantum search of a database any easier?
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
An optical model of computation
Theoretical Computer Science
Quantum and classical complexity classes: separations, collapses, and closure properties
Information and Computation
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
Universal test for quantum one-way permutations
Theoretical Computer Science - Mathematical foundations of computer science 2004
Quantum and classical tradeoffs
Theoretical Computer Science
On the Complexity of Searching for a Maximum of a Function on a Quantum Computer
Quantum Information Processing
Limitations of quantum coset states for graph isomorphism
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Quantum lower bounds for the Goldreich-Levin problem
Information Processing Letters
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
Revisiting a limit on efficient quantum computation
Proceedings of the 44th annual Southeast regional conference
Hybrid quantum-classical computing with applications to computer graphics
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
The Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries
Quantum Information Processing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Existence Testing and Its Application for Finding Extreme Values in Unsorted Databases
IEEE Transactions on Computers
An R || Cmax Quantum Scheduling Algorithm
Quantum Information Processing
Quantum Partial Search of a Database with Several Target Items
Quantum Information Processing
Quantum certificate complexity
Journal of Computer and System Sciences
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Evolving blackbox quantum algorithms using genetic programming
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Cryptography Based on Quadratic Forms: Complexity Considerations
Research in Cryptology
Parallel and Sequential Optical Computing
OSC '08 Proceedings of the 1st international workshop on Optical SuperComputing
A new connection between quantum circuits, graphs and the Ising partition function
Quantum Information Processing
Quantum Algorithms for Evaluating Min-Max Trees
Theory of Quantum Computation, Communication, and Cryptography
Quantum approaches to graph colouring
Theoretical Computer Science
Quantum resistant public key cryptography: a survey
Proceedings of the 8th Symposium on Identity and Trust on the Internet
A review of procedures to evolve quantum algorithms
Genetic Programming and Evolvable Machines
On the solution of trivalent decision problems by quantum state identification
Natural Computing: an international journal
Quantum and classical complexity classes: Separations, collapses, and closure properties
Information and Computation
Quantum lower bounds for the Goldreich--Levin problem
Information Processing Letters
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
The geometry of quantum learning
Quantum Information Processing
Can quantum search accelerate evolutionary algorithms?
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Time space tradeoffs for attacks against one-way functions and PRGs
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Relativized worlds without worst-case to average-case reductions for NP
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Spatial search on a honeycomb network
Mathematical Structures in Computer Science
A Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem
SIAM Journal on Scientific Computing
Quantum Information Processing
Tree search and quantum computation
Quantum Information Processing
The quantum query complexity of certification
Quantum Information & Computation
Counting, fanout and the complexity of quantum ACC
Quantum Information & Computation
On quantum one-way permutations
Quantum Information & Computation
How significant are the known collision and element distinctness quantum algorithms
Quantum Information & Computation
Quantum computing and polynomial equations over the finite field Z2
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
Hidden symmetry detection on a quantum computer
Quantum Information & Computation
Exact quantum lower bound for grover's problem
Quantum Information & Computation
The geometry of quantum computation
Quantum Information & Computation
Merkle puzzles in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
SIAM Journal on Computing
How many query superpositions are needed to learn?
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Zero-knowledge proof of generalized compact knapsacks (or a novel identification/signature scheme)
ATC'06 Proceedings of the Third international conference on Autonomic and Trusted Computing
Quantum search in a possible three-dimensional complex subspace
Quantum Information Processing
Quantum Information Processing
Can quantum entanglement detection schemes improve search?
Quantum Information Processing
Knot theory, jones polynomial and quantum computing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Bounds on the power of constant-depth quantum circuits
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Spatial search using the discrete time quantum walk
Natural Computing: an international journal
General Theory of Information Transfer and Combinatorics
An upper bound on the rate of information transfer by grover's oracle
General Theory of Information Transfer and Combinatorics
Random oracles in a quantum world
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
A novel image encryption/decryption scheme based on chaotic neural networks
Engineering Applications of Artificial Intelligence
Quantum money from hidden subspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The quantum query complexity of AC0
Quantum Information & Computation
Impossibility of succinct quantum proofs for collision-freeness
Quantum Information & Computation
Black-box hamiltonian simulation and unitary implementation
Quantum Information & Computation
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
ACM Transactions on Computation Theory (TOCT)
Improving quantum query complexity of boolean matrix multiplication using graph collision
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Quantum speed-up for unsupervised learning
Machine Learning
Quantum search with certainty based on modified Grover algorithms: optimum choice of parameters
Quantum Information Processing
Reduction from non-injective hidden shift problem to injective hidden shift problem
Quantum Information & Computation
Quantum entanglement and the communication complexity of the inner product function
Theoretical Computer Science
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
A universal quantum circuit scheme for finding complex eigenvalues
Quantum Information Processing
Quantum Information Processing
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Recently a great deal of attention has been focused on quantum computation following a sequence of results [Bernstein and Vazirani, in Proc. 25th Annual ACM Symposium Theory Comput., 1993, pp. 11--20, SIAM J. Comput., 26 (1997), pp. 1277--1339], [Simon, in Proc. 35th Annual IEEE Symposium Foundations Comput. Sci., 1994, pp. 116--123, SIAM J. Comput., 26 (1997), pp. 1340--1349], [Shor, in Proc. 35th Annual IEEE Symposium Foundations Comput. Sci., 1994, pp. 124--134] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time, it is natural to ask whether all of $\NP$ can be efficiently solved in quantum polynomial time. In this paper, we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$. We also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class $\NP \cap \coNP$ cannot be solved on a QTM in time $o(2^{n/3})$. The former bound is tight since recent work of Grover [in {\it Proc.\ $28$th Annual ACM Symposium Theory Comput.}, 1996] shows how to accept the class $\NP$ relative to any oracle on a quantum computer in time $O(2^{n/2})$.