We present a quantum algorithm that verifies a product of two <i>n</i> Ã— <i>n</i> matrices over any integral domain with bounded error in worst-case time <i>O</i>(<i>n</i><sup>5/3</sup>) and expectedâ€¦ (More)

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 toâ€¦ (More)

We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf ) canâ€¦ (More)

We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf ) canâ€¦ (More)

2011 IEEE 52nd Annual Symposium on Foundations ofâ€¦

2011

State conversion generalizes query complexity to the problem of converting between two input-dependent quantum states by making queries to the input. We characterize the complexity of this problem byâ€¦ (More)

We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulasâ€¦ (More)

We present quantum algorithms for some graph problems: finding a maximal bipartite matching in time O(n âˆš m logn), finding a maximal non-bipartite matching in time O(n( âˆš m/n+logn) logn), and findingâ€¦ (More)

2008 23rd Annual IEEE Conference on Computationalâ€¦

2008

Discrepancy is a versatile bound in communication complexity which can be used to show lower bounds in randomized, quantum, and even weakly-unbounded error models of communication. We show an optimalâ€¦ (More)