#### Filter Results:

#### Publication Year

1998

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn 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)

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)

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring Z[ 1 √ 2 , i], in the single-qubit case. We report an efficient synthesis algorithm, with an exact optimality guarantee on the number of Hadamard and T gates used. We conjecture that the equivalence… (More)

According to the web site, at the recent 2007 Federated Computing Research Conference, Christos Papadimitriou from UC Berkeley gave a talk on how computer science is transforming the sciences. The first sentence of his abstract states that: Computational research transforms the sciences (physical, mathematical, life or social) not just by empowering them… (More)

We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speed-up over simple brute force algorithms. As an illustration of our method we implemented this algorithm and found factorizations of the commonly used quantum logical operations into elementary gates… (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)

A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, sta-bilisers 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)

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

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)