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In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1/2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition…
Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^\alpha$, $1<\alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a…
We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz and Mattis to non-interacting fermions, we can obtain a numerically exact solution for rather…
We analyze the popular ``state-space'' class of algorithms for detecting casual interaction in coupled dynamical systems. These algorithms are often justified by Takens' embedding theorem, which provides conditions under which relationships…
Distribution network operation is becoming more challenging because of the growing integration of intermittent and volatile distributed energy resources (DERs). This motivates the development of new distribution system state estimation…
Finding an energy minimum in the Ising model is an exemplar objective, associated with many combinatorial optimization problems, that is computationally hard in general, but occurs in all areas of modern science. There are several numerical…
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement…
We present a general strategy to extend quantum cluster algorithms for S=1/2 spin systems, such as the loop algorithm, to systems with arbitrary size of spins. In general, the partition function of a high-S spin system is represented in…
The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a…
Current transmission and distribution system states are mostly unobservable to each other, and state estimation is separately conducted in the two systems owing to the differences in network structures and analytical models. The large-scale…