The field of classical stochastic processes forms a major branch of mathematics. Stochastic
processes are, of course, also very well studied in biology, chemistry, ecology, geology …

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally
relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated …

Characterization protocols have so far played a central role in the development of noisy
intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This …

In the path integral formulation of the evolution of an open quantum system coupled to a
Gaussian, noninteracting environment, the dynamical contribution of the latter is encoded in …

In the classical domain, it is well known that divisibility does not imply that a stochastic
process is Markovian. However, for quantum processes, divisibility is often considered to be …

Machine learning methods have proved to be useful for the recognition of patterns in
statistical data. The measurement outcomes are intrinsically random in quantum physics …

Quantum metrology is a rapidly developing branch of quantum technologies. While various
theories have been established on quantum metrology for Markovian processes, ie …

We show how a tensor-network-based machine learning algorithm can learn the structures
of generic, non-Markovian, quantum stochastic processes. First, a process is represented as …

Non-Markovian quantum processes exhibit different memory effects when measured in
different ways; an unambiguous characterization of memory length requires accounting for …

Estimating the features of noise is the first step in a chain of protocols that will someday lead
to fault-tolerant quantum computers. The randomized benchmarking (RB) protocol is …