Related papers: Accessing the dynamics of large many-particle syst…
The stochastic Schr\"odinger equation (SSE) provides a trajectory-level route to simulate the dynamics of open quantum systems with applications ranging from molecular processes to quantum technologies. We study a colored-noise extension of…
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or…
Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
We present a new non-local updating scheme for quantum Monte Carlo simulations, which conserves particle number and other symmetries. It allows exact symmetry projection and direct evaluation of the equal-time Green's function and other…
Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…
The cross entropy (CE) method is a model based search method to solve optimization problems where the objective function has minimal structure. The Monte-Carlo version of the CE method employs the naive sample averaging technique which is…
Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state…
Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling's performance is highly sensitive to the…
One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions,…
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term…
We propose a stochastic Schr\"odinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely insufficient exploration on continuous coupling and…
Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multi-qubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic…
The estimation of all the parameters in an unknown quantum state or measurement device, commonly known as quantum state tomography (QST) and quantum detector tomography (QDT), is crucial for comprehensively characterizing and controlling…