Related papers: Classical spin models and the quantum stabilizer f…
We investigate the possibility of simulating partially entangled two qubit states by separable states of higher spins. First, we show that all partially entangled isotropic states can be simulated classically. We further investigate…
Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We investigate dynamics of semi-quantal spin systems in which quantum bits are attached to classically and possibly stochastically moving classical particles. The interaction between the quantum bits takes place when the respective…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
The spin of an electron trapped in a quantum dot is a promising candidate implementation of a qubit for quantum information processing. We study the central spin problem of the effect of the hyperfine interaction between such an electron…
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second,…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…
We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by means of a set of equations resembling the…
We analyze the behaviour of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…