Related papers: Universal Quantum Hamiltonians
Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is…
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we…
We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom,…
We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system…
In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard…
Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
We consider fully many-body localized systems, i.e. isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators.…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\bf R}_A$ and ${\bf P}_A,\; A=1,\ldots,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian…
We discusse a relativistic Hamiltonian for an n-body problem in which all the masses are equal and all spins take value 1/2. In the frame of reference in which the total momentum $\v{P}=0$, the Foldy-Wouthuysen transformation is applies and…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…