Related papers: Learning conservation laws in unknown quantum dyna…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
It is shown how S-matrix theory and the concept of continuous quantum measurements can be combined to yield Markovian master equations which describe the environmental interaction non-perturbatively. The method is then applied to obtain the…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation…
We demonstrate that the dynamics of quantum coherence serves as an effective probe for identifying dephasing, which is a distinctive signature of many-body localization (MBL). Quantum coherence can be utilized to measure both the local…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized…
The area law-like scaling of local quantum entropies is the central characteristic of the entanglement inherent in quantum fields, many-body systems, and spacetime. Whilst the area law is primarily associated with the entanglement structure…
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve…
We have applied a machine learning algorithm to predict the emergence of environment-induced spontaneous synchronization between two qubits in an open system setting. In particular, we have considered three different models, encompassing…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
The ability to harness the dynamics of quantum information and entanglement is necessary for the development of quantum technologies and the study of complex quantum systems. On the theoretical side the dynamics of quantum information is a…
The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm…
Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids and glasses. The conundrum: close to the glass transition, the dynamics slow down…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…