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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)

- Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, Ronald de Wolf
- J. ACM
- 1998

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)

Quantum computers use the quantum interference of diierent computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identiied when quantum computation is viewed as multi-particle interference. We use this approach to review (and improve) some of the existing… (More)

- Wim van Dam, Michele Mosca, Umesh V. Vazirani
- FOCS
- 2001

We analyze the computational power and limitations of the recently proposed ‘quantum adiabatic evolution algorithm’.

- Andris Ambainis, Michele Mosca, Alain Tapp, Ronald de Wolf
- FOCS
- 2000

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)

- Kevin K. H. Cheung, Michele Mosca
- Quantum Information & Computation
- 2001

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)

- Matthew Amy, Dmitri Maslov, Michele Mosca, Martin Rötteler
- IEEE Transactions on Computer-Aided Design of…
- 2013

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)

- Peter Høyer, Michele Mosca, Ronald de Wolf
- ICALP
- 2003

Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O( √ n) repetitions of the base algorithms and with high probability finds the index of a 1-bit among these n bits (if there is such an index). This shows that it is not necessary to first significantly… (More)

Quite justifiably, one of his examples was quantum computing. I am quite sure that the regular contributors to this journal would agree: our view of quantum mechanics has been transformed by the efforts of our pioneering colleagues in computer science. This helpful little book by Kaye, Laflamme and Mosca is an attempt to bring this new view to a wider… (More)

- Michele Mosca, Artur Ekert
- QCQC
- 1998

A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and hidden or unknown subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the… (More)