Related papers: Mean-field equations for higher-order quantum stat…
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
In this work, we show that the quantum compass model on an square lattice can be mapped to a fermionic model with local density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular…
We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…
Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be…
We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents…
We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field…
Characterizing correlations in a quantum system on the basis of the results of the projective measurements can be performed with different means including the calculation of the classical mutual information. Generally, estimating such…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a…
Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
This manuscript provides a general approach to the investigation of field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in…
This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior…