774 research outputs found
Solving Set Cover with Pairs Problem using Quantum Annealing
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with
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
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