Related papers: Quantum-Guided Cluster Algorithms for Combinatoria…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite…
The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are…
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are…
Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
Working within the Stochastic Series Expansion (SSE) framework, we construct efficient quantum cluster algorithms for transverse field Ising antiferromagnets on the pyrochlore lattice and the planar pyrochlore lattice, for the fully…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…
Finding the ground state of spin glasses is a challenging problem with broad implications. Many hard optimization problems, including NP-complete problems, can be mapped, for instance, to the Ising spin glass model. We present a graph-based…
We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of…
Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning--assisted approaches are…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…