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Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe…
We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of…
Accurate power system state estimation (PSSE) is an essential prerequisite for reliable operation of power systems. Different from static PSSE, dynamic PSSE can exploit past measurements based on a dynamical state evolution model, offering…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an…
We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…
The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…
One of the most promising applications of near-term quantum computing is the simulation of quantum systems, a classically intractable task. Quantum simulation requires computationally expensive matrix exponentiation; Trotter-Suzuki…
We present a universal framework for simulating $N$-dimensional linear It\^o stochastic differential equations (SDEs) on quantum computers with additive or multiplicative noises. Building on a unitary dilation technique, we establish a…
Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield…
In this paper, we propose an approach for an application of Bayesian optimization using Sequential Monte Carlo (SMC) and concepts from the statistical physics of classical systems. Our method leverages the power of modern machine learning…
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE…
Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…
In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…
Ab initio quantum chemistry calculations for systems with large active spaces are notoriously difficult and cannot be successfully tackled by standard methods. In this letter, we generalize a Green's function QM/QM embedding method called…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state space models, but offer an alternative to MCMC in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC…
Power system simulations that extend over a time period of minutes, hours, or even longer are called extended-term simulations. As power systems evolve into complex systems with increasing interdependencies and richer dynamic behaviors…