Related papers: Quantum coarse-graining for extreme dimension redu…

Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…

Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of…

The common idea behind complexity reduction in physical systems is separation of information into "physically meaningful" and "safely ignorable". Here we consider a generic notion of such separation -- implemented by coarse-graining the…

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…

The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is…

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…

Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of…

Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g. traffic congestion, are effectively probabilistic because we…

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…

Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

Effective and efficient forecasting relies on identification of the relevant information contained in past observations -- the predictive features -- and isolating it from the rest. When the future of a process bears a strong dependence on…

Quantum state tomography often operates in the highly idealised scenario of assuming perfect measurements. The errors implied by such an approach are entwined with other imperfections relating to the information processing protocol or…

We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the…

Quantum machine learning provides a fundamentally different approach to analyzing data. However, many interesting datasets are too complex for currently available quantum computers. Present quantum machine learning applications usually…

Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their…