34,297 research outputs found
A Novel Clustering Algorithm Based on Quantum Games
Enormous successes have been made by quantum algorithms during the last
decade. In this paper, we combine the quantum game with the problem of data
clustering, and then develop a quantum-game-based clustering algorithm, in
which data points in a dataset are considered as players who can make decisions
and implement quantum strategies in quantum games. After each round of a
quantum game, each player's expected payoff is calculated. Later, he uses a
link-removing-and-rewiring (LRR) function to change his neighbors and adjust
the strength of links connecting to them in order to maximize his payoff.
Further, algorithms are discussed and analyzed in two cases of strategies, two
payoff matrixes and two LRR functions. Consequently, the simulation results
have demonstrated that data points in datasets are clustered reasonably and
efficiently, and the clustering algorithms have fast rates of convergence.
Moreover, the comparison with other algorithms also provides an indication of
the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table
Coreset Clustering on Small Quantum Computers
Many quantum algorithms for machine learning require access to classical data
in superposition. However, for many natural data sets and algorithms, the
overhead required to load the data set in superposition can erase any potential
quantum speedup over classical algorithms. Recent work by Harrow introduces a
new paradigm in hybrid quantum-classical computing to address this issue,
relying on coresets to minimize the data loading overhead of quantum
algorithms. We investigate using this paradigm to perform -means clustering
on near-term quantum computers, by casting it as a QAOA optimization instance
over a small coreset. We compare the performance of this approach to classical
-means clustering both numerically and experimentally on IBM Q hardware. We
are able to find data sets where coresets work well relative to random sampling
and where QAOA could potentially outperform standard -means on a coreset.
However, finding data sets where both coresets and QAOA work well--which is
necessary for a quantum advantage over -means on the entire data
set--appears to be challenging
Multistart Methods for Quantum Approximate Optimization
Hybrid quantum-classical algorithms such as the quantum approximate
optimization algorithm (QAOA) are considered one of the most promising
approaches for leveraging near-term quantum computers for practical
applications. Such algorithms are often implemented in a variational form,
combining classical optimization methods with a quantum machine to find
parameters to maximize performance. The quality of the QAOA solution depends
heavily on quality of the parameters produced by the classical optimizer.
Moreover, the presence of multiple local optima in the space of parameters
makes it harder for the classical optimizer. In this paper we study the use of
a multistart optimization approach within a QAOA framework to improve the
performance of quantum machines on important graph clustering problems. We also
demonstrate that reusing the optimal parameters from similar problems can
improve the performance of classical optimization methods, expanding on similar
results for MAXCUT
Quantum jet clustering with LHC simulated data
We study the case where quantum computing could improve jet clustering by
considering two new quantum algorithms that might speed up classical jet
clustering algorithms. The first one is a quantum subroutine to compute a
Minkowski-based distance between two data points, while the second one consists
of a quantum circuit to track the rough maximum into a list of unsorted data.
When one or both algorithms are implemented in classical versions of well-known
clustering algorithms (K-means, Affinity Propagation and -jet) we obtain
efficiencies comparable to those of their classical counterparts. Furthermore,
in the first two algorithms, an exponential speed up in dimensionality and data
length can be achieved when applying the distance or the maximum search
algorithm. In the algorithm, a quantum version of the same order as
FastJet is achieved.Comment: 6 pages, 1 figure, 1 table, Contribution to 41st International
Conference on High Energy physics - ICHEP 2022, 6-13 July 2022, Bologna,
Ital
Clustering of Conditional Mutual Information for Quantum Gibbs States above a Threshold Temperature
We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the exponential decay for short-ranged interacting systems and power-law decay for long-ranged interacting systems. Consequently, we establish the efficiency of quantum Gibbs sampling algorithms, a strong version of the area law, the quasilocality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulations
Quantum Motif Clustering
We present three quantum algorithms for clustering graphs based on
higher-order patterns, known as motif clustering. One uses a straightforward
application of Grover search, the other two make use of quantum approximate
counting, and all of them obtain square-root like speedups over the fastest
classical algorithms in various settings. In order to use approximate counting
in the context of clustering, we show that for general weighted graphs the
performance of spectral clustering is mostly left unchanged by the presence of
constant (relative) errors on the edge weights. Finally, we extend the original
analysis of motif clustering in order to better understand the role of multiple
`anchor nodes' in motifs and the types of relationships that this method of
clustering can and cannot capture.Comment: 51 pages, 11 figure
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