Related papers: Graphical method in loop quantum gravity: I. Deriv…
We present a novel way to manipulate ultra-cold atoms where four atomic levels are trapped by appropriately tuned optical lattices. When employed to perform quantum computation via global control, this unique structure dramatically reduces…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in…
We carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and couplings, etc. which include the class of quantum…
We embark on the vast program of integrating the dynamics of Loop Quantum Gravity (LQG). Adopting the strategy of decomposing spin network states into small blocks of (quantum) geometry which can later be glued back together, we focus on…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the…
In this work, we propose a generalization of the current most widely used quantum computing hardware metric known as the quantum volume. The quantum volume specifies a family of random test circuits defined such that the logical circuit…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the…
Using Penrose binor calculus for $SU(2)$ ($SL(2,C)$) tensor expressions, a graphical method for the connection representation of Euclidean Quantum Gravity (real connection) is constructed. It is explicitly shown that: {\it (i)} the recently…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…