Related papers: More on complexity of operators in quantum field t…
We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include…
Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts…
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…
The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
By analogy with the invariant Q-category defined by Scheerer, Stanley and Tanr\'e, we introduce the notions of Q-sectional category and Q-topological complexity. We establish several properties of these invariants. We also obtain a formula…
Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the…
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…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
By considering matter as a constraint on the availability of gravitational degrees of freedom and accounting for the statistical interpretation of Rindler horizons, the freedom to construct quantum gravity theories reproducing General…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…