Stochastic processes are as ubiquitous throughout the quantitative sciences as they are
notorious for being difficult to simulate and predict. In this Letter, we propose a unitary …

The principle goal of computational mechanics is to define pattern and structure so that the
organization of complex systems can be detected and quantified. Computational mechanics …

Causal asymmetry is one of the great surprises in predictive modeling: The memory required
to predict the future differs from the memory required to retrodict the past. There is 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 …

In stochastic modeling, the excess entropy--the mutual information shared between a
processes past and future--represents the fundamental lower bound of the memory needed …

Isolating past information relevant for future prediction is central to quantitative science.
Quantum models offer a promising approach, enabling statistically faithful modeling while …

We introduce a quantum algorithm for memory-efficient biased sampling of rare events
generated by classical memoryful stochastic processes. Two efficiency metrics are used to …

In stochastic modeling, there has been a significant effort towards finding predictive models
that predict a stochastic process' future using minimal information from its past. Meanwhile …

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 …

Stochastic processes underlie a vast range of natural and social phenomena. Some
processes such as atomic decay feature intrinsic randomness, whereas other complex …