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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)

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 the… (More)

- R Cleve, A Ekert, C Macchiavello, M Mosca
- 1997

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)

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)

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

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)

We examine the number T of oracle calls that a quantum network requires to compute some Boolean function on {0, 1} N in the so-called black-box model, where the input is given as an oracle. We show that the acceptance probability of a network can be written as an N-variate polynomial of the input, having degree at most 2T. Using lower bounds on the degrees… (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)

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)