Related papers: Memory Complexity of Quantum Processes
Accurately quantifying the thermodynamic work costs of quantum operations is essential for the continued development and optimisation of emerging quantum technologies. This present a significant challenge in regimes of rapid control within…
We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for…
Among the predictive hidden Markov models that describe a given stochastic process, the {\epsilon}-machine is strongly minimal in that it minimizes every R\'enyi-based memory measure. Quantum models can be smaller still. In contrast with…
Memory effects play a fundamental role in the study of the dynamics of open quantum systems. There exist two conceptually distinct notions of memory discussed for quantum channels in the literature. In quantum information theory quantum…
By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a whole host of computational advantages. One such advantage lies in the field of stochastic modelling, where it has been shown that quantum stochastic…
Any real interaction process produces many incompatible system versions, or realisations, giving rise to omnipresent dynamic randomness and universally defined complexity (arXiv:physics/9806002). Since quantum behaviour dynamically emerges…
We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and…
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this…
Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and…
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
Forgetfulness is a common feature of nature. Moreover, without forgetfulness, repeatability would be impossible. Despite this, small systems constantly leak information about their state to their surroundings, and quantum mechanics tells us…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
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…
We consider a recently introduced framework for the description of memory effects based on quantum state distinguishability quantifiers, in which entropic quantifiers can be included. After briefly presenting the approach, we validate it…
The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…