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\kmeans clustering is a fundamental problem in many scientific and engineering domains. The optimization problem associated with \kmeans clustering is nonconvex, for which standard algorithms are only guaranteed to find a local optimum.…
High-fidelity measurements are important for the physical implementation of quantum information protocols. Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities that are systematically…
We discuss a new Monte Carlo algorithm for the simulation of complex fluids. This algorithm employs geometric operations to identify clusters of particles that can be moved in a rejection-free way. It is demonstrated that this geometric…
Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this paper, we propose a novel QEM…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges…
We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…
This article introduces a novel approach to perform the simulation of a single qubit quantum algorithm using laser beams. Leveraging the polarization states of photonic qubits, and inspired by variational quantum eigensolvers, we develop a…
Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We…
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available.…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
Quantum dimer model is a low-energy and efficient model to study quantum spin systems and strong-correlated physics. As a foreseeing step and without loss of generality, we study the classical dimers on square lattice by means of Monte…
We perform numerical tests on quantum nonlocality of two-level quantum systems (qubits) observed by a uniformly moving observer. Under a suitable momentum setting, the quantum nonlocality of two-qubit nonmaximally entangled states could be…
We present an approach to design stabilizing controllers for a set of linear systems without restrictions regarding their modeling order. To this end, the systems are treated as abstract objects in the space of the $\nu$-gap metric. Via a…