Michele Mosca

Learn More
Consider a Boolean function χ : X → {0, 1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A|0〉 = ∑ x∈X αx|x〉 is a quantum superposition of the elements of X, and let a denote the probability that a good element is produced if A|0〉 is measured. If we repeat(More)
We examine the number of queries to input variables that a quantum algorithm requires to compute Boolean functions on {0,1}<i><sup>N</sup></i> in the <i>black-box</i> model. We show that the exponential quantum speed-up obtained for <i>partial</i> functions (i.e., problems involving a promise on the input) by Deutsch and Jozsa, Simon, and Shor cannot be(More)
We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of(More)
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as(More)
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute force algorithms. As an illustration of our method, we implemented this algorithm and found factorizations of commonly used quantum logical operations into elementary gates in(More)