4,093 research outputs found
New Developments in Quantum Algorithms
In this survey, we describe two recent developments in quantum algorithms.
The first new development is a quantum algorithm for evaluating a Boolean
formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This
provides quantum speedups for any problem that can be expressed via Boolean
formulas. This result can be also extended to span problems, a generalization
of Boolean formulas. This provides an optimal quantum algorithm for any Boolean
function in the black-box query model.
The second new development is a quantum algorithm for solving systems of
linear equations. In contrast with traditional algorithms that run in time
O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in
time O(\log^c N). It outputs a quantum state describing the solution of the
system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201
Multiple Query Optimization on the D-Wave 2X Adiabatic Quantum Computer
The D-Wave adiabatic quantum annealer solves hard combinatorial optimization
problems leveraging quantum physics. The newest version features over 1000
qubits and was released in August 2015. We were given access to such a machine,
currently hosted at NASA Ames Research Center in California, to explore the
potential for hard optimization problems that arise in the context of
databases.
In this paper, we tackle the problem of multiple query optimization (MQO). We
show how an MQO problem instance can be transformed into a mathematical formula
that complies with the restrictive input format accepted by the quantum
annealer. This formula is translated into weights on and between qubits such
that the configuration minimizing the input formula can be found via a process
called adiabatic quantum annealing. We analyze the asymptotic growth rate of
the number of required qubits in the MQO problem dimensions as the number of
qubits is currently the main factor restricting applicability. We
experimentally compare the performance of the quantum annealer against other
MQO algorithms executed on a traditional computer. While the problem sizes that
can be treated are currently limited, we already find a class of problem
instances where the quantum annealer is three orders of magnitude faster than
other approaches
Discrete-Query Quantum Algorithm for NAND Trees
This is a comment on the article “A Quantum Algorithm for the Hamiltonian NAND Tree” by Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, Theory of Computing 4 (2008) 169--190. That paper gave a quantum algorithm for evaluating NAND trees with running time O(√N) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using N^[1/2 + o(1)] queries in the conventional (discrete) quantum query model
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