Related papers: Graphical calculus of spin networks
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally…
Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings…
In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a consequence, quantum states of the bulk geometry needs to be…
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…
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase…
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…
An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is…
To clarify the geometric information encoded in the $SO(D+1)$ spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the $SU(2)$ phase space for $(1+3)$ dimensional loop…
A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…
We give for the first time a diagrammatic calculational tool of quantum entanglement. We present a pedagogical and simple mechanical implementation of quantum entanglement or "spooky action at a distance" to give a tangible realization of…
Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity.…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor…
In this note, variational Monte Carlo method based on neural quantum states for spin systems is reviewed. Using a neural network as the wave function allows for a more generalized expression of various types of interactions, including…
We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy,…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…