69 research outputs found
Parallel Quantum Annealing
Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute
high quality solutions of NP-hard problems. This is done by mapping a problem
onto the physical qubits of the quantum chip, from which a solution is obtained
after quantum annealing. However, since the connectivity of the physical qubits
on the chip is limited, a minor embedding of the problem structure onto the
chip is required. In this process, and especially for smaller problems, many
qubits will stay unused. We propose a novel method, called parallel quantum
annealing, to make better use of available qubits, wherein either the same or
several independent problems are solved in the same annealing cycle of a
quantum annealer, assuming enough physical qubits are available to embed more
than one problem. Although the individual solution quality may be slightly
decreased when solving several problems in parallel (as opposed to solving each
problem separately), we demonstrate that our method may give dramatic speed-ups
in terms of Time-to-Solution (TTS) for solving instances of the Maximum Clique
problem when compared to solving each problem sequentially on the quantum
annealer. Additionally, we show that solving a single Maximum Clique problem
using parallel quantum annealing reduces the TTS significantly.Comment: 13 pages. v4: format improvement
Towards Solving the Navier-Stokes Equation on Quantum Computers
In this paper, we explore the suitability of upcoming novel computing
technologies, in particular adiabatic annealing based quantum computers, to
solve fluid dynamics problems that form a critical component of several science
and engineering applications. We start with simple flows with well-studied flow
properties, and provide a framework to convert such systems to a form amenable
for deployment on such quantum annealers. We analyze the solutions obtained
both qualitatively and quantitatively as well as the sensitivities of the
various solution selection schemes on the obtained solution
Most Frequent Itemset Optimization
In this paper we are dealing with the frequent itemset mining. We concentrate
on the special case that we only want to identify the most frequent itemset of
length N. To do that, we present a pattern on how to consider this search as an
optimization problem. First, we extract the frequency of all possible
2-item-sets. Then the optimization problem is to find the N objects, for which
the minimal frequency of all containing 2-item-sets is maximal. This
combinatorial optimization problem can be solved by any optimization algorithm.
We will solve them with Quantum Annealing and QUBO with QbSolv by D-Wave. The
advantages of MFIO in comparison to the state-of-the-art-approach are the
enormous reduction of time need, reduction of memory need and the omission of a
threshold. The disadvantage is that there is no guaranty for accuracy of the
result. The evaluation indicates good results
Comparing Three Generations of D-Wave Quantum Annealers for Minor Embedded Combinatorial Optimization Problems
Quantum annealing is a novel type of analog computation that aims to use
quantum mechanical fluctuations to search for optimal solutions of Ising
problems. Quantum annealing in the Transverse Ising model, implemented on
D-Wave QPUs, are available as cloud computing resources. In this article we
report concise benchmarks across three generations of D-Wave quantum annealers,
consisting of four different devices, for the NP-Hard combinatorial
optimization problems unweighted maximum clique and unweighted maximum cut on
random graphs. The Ising, or equivalently QUBO, formulation of these problems
do not require auxiliary variables for order reduction, and their overall
structure and weights are not highly complex, which makes these problems simple
test cases to understand the sampling capability of current D-Wave quantum
annealers. All-to-all minor embeddings of size , with relatively uniform
chain lengths, are used for a direct comparison across the Chimera, Pegasus,
and Zephyr device topologies. A grid search over annealing times and the minor
embedding chain strengths is performed in order to determine the level of
reasonable performance for each device and problem type. Experiment metrics
that are reported are approximation ratios for non-broken chain samples and
chain break proportions. How fairly the quantum annealers sample optimal
maximum cliques, for instances which contain multiple maximum cliques, is also
quantified using entropy of the measured ground state distributions. The newest
generation of quantum annealing hardware, which has a Zephyr hardware
connectivity, performed the best overall with respect to approximation ratios
and chain break frequencies
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