Related papers: Learning Generalized Statistical Mechanics with Ma…
We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs…
The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…
We describe a novel algorithm that learns a Hamiltonian from local expectations of its Gibbs state using the free energy variational principle. The algorithm avoids the need to compute the free energy directly, instead using efficient…
In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…
We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
We propose a statistical mechanics for a general class of stationary and metastable equilibrium states. For this purpose, the Gibbs extremal conditions are slightly modified in order to be applied to a wide class of non-equilibrium states.…
We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra…
Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite…
A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…
Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…