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Quantum computers and simulators promise to enable the study of strongly correlated quantum systems. Yet, surprisingly, it is hard for them to compute ground states. They can, however, efficiently compute the dynamics of closed quantum…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
We present a first principles molecular dynamics approach that is based on time-reversible ex- tended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field…
The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled,…
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive…
We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Quantum hydrodynamic theory (QHT) can describe some of the characteristic features of quantum electron dynamics that appear in metallic nanostructures, such as spatial nonlocality, electron spill-out, and quantum tunneling. Furthermore,…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Graph states are computationally powerful quantum states with many applications including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analogue…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
This study applies response theory to investigate electron charge dynamics, with a particular focus on charge separation. We analytically assess the strengths and limitations of linear and quadratic response theories in describing charge…
Here, we propose a platform based on ultra-cold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems. The idea consists of a judicious choice of two…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the…
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…