305 research outputs found
On the solution of trivalent decision problems by quantum state identification
The trivalent functions of a trit can be grouped into equipartitions of three
elements. We discuss the separation of the corresponding functional classes by
quantum state identifications
How many functions can be distinguished with k quantum queries?
Suppose an oracle is known to hold one of a given set of D two-valued
functions. To successfully identify which function the oracle holds with k
classical queries, it must be the case that D is at most 2^k. In this paper we
derive a bound for how many functions can be distinguished with k quantum
queries.Comment: 5 pages. Lower bound on sorting n items improved to (1-epsilon)n
quantum queries. Minor changes to text and corrections to reference
Query complexity for searching multiple marked states from an unsorted database
An important and usual problem is to search all states we want from a
database with a large number of states. In such, recall is vital. Grover's
original quantum search algorithm has been generalized to the case of multiple
solutions, but no one has calculated the query complexity in this case. We will
use a generalized algorithm with higher precision to solve such a search
problem that we should find all marked states and show that the practical query
complexity increases with the number of marked states. In the end we will
introduce an algorithm for the problem on a ``duality computer'' and show its
advantage over other algorithms.Comment: 4 pages,4 figures,twocolum
Two Classical Queries versus One Quantum Query
In this note we study the power of so called query-limited computers. We
compare the strength of a classical computer that is allowed to ask two
questions to an NP-oracle with the strength of a quantum computer that is
allowed only one such query. It is shown that any decision problem that
requires two parallel (non-adaptive) SAT-queries on a classical computer can
also be solved exactly by a quantum computer using only one SAT-oracle call,
where both computations have polynomial time-complexity. Such a simulation is
generally believed to be impossible for a one-query classical computer. The
reduction also does not hold if we replace the SAT-oracle by a general
black-box. This result gives therefore an example of how a quantum computer is
probably more powerful than a classical computer. It also highlights the
potential differences between quantum complexity results for general oracles
when compared to results for more structured tasks like the SAT-problem.Comment: 6 pages, LaTeX2e, no figures, minor changes and correction
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