Related papers: Noncomputability Arising In Dynamical Triangulatio…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are…
In this paper we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples ${(\mathcal{A},…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems…
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best…
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…
The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group;…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
We show that, in two-dimensional Euclidean quantum gravity without matter fields, the Schwinger-Dyson equations derived within the Hamiltonian framework of non-critical string field theory can be reformulated in terms of the…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is contractible in M. Our algorithm runs in space polynomial in…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
We discuss the counting of minimal geodesic ball coverings of $n$-dimensional riemannian manifolds of bounded geometry, fixed Euler characteristic and Reidemeister torsion in a given representation of the fundamental group. This counting…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative…
We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the…
In this paper explore the relation between covariant and canonical approaches to quantum gravity and $BF$ theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of…
Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…