Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Communication complexity
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Polynomial Degree vs. Quantum Query Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS
Computational Complexity
On the power of Ambainis lower bounds
Theoretical Computer Science
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theoretical Computer Science
Lower bounds on quantum query complexity for read-once decision trees with parity nodes
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Breaking the rectangle bound barrier against formula size lower bounds
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
The quantum query complexity of certification
Quantum Information & Computation
Quantum interpolation of polynomilas
Quantum Information & Computation
Merkle puzzles in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Faster quantum algorithm for evaluating game trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A stronger LP bound for formula size lower bounds via clique constraints
Theoretical Computer Science
Improving quantum clocks via semidefinite programming
Quantum Information & Computation
The quantum query complexity of AC0
Quantum Information & Computation
Quantum adversary (upper) bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Quantum counterfeit coin problems
Theoretical Computer Science
Adversary lower bound for the k-sum problem
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Properties and applications of boolean function composition
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Superlinear advantage for exact quantum algorithms
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
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The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower bounds, and is versatile with equivalent formulations interms of weight schemes, eigen values, and Kolmogorov complexity. All these formulations rely on the principlethat if an algorithm successfully computes a function then, in particular, itis able to distinguish between inputs which map to different values. We present a stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function. This new method, which we call ADV+-, has all the advantages ofthe old: it is a lower bound on bounded-error quantum query complexity, its square is a lower bound on formula size, and it behaves well with respect tofunction composition. Moreover ADV+- is always at least as large as the adversary method ADV, and we show an example of a monotone function forwhich ADV+-(f)=Omega(ADV(f)1.098). We also give examples showing that ADV+- does not face limitations of ADV like the certificate complexity barrier and the property testing barrier.