Related papers: On Holant Theorem and Its Proof
In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the…
It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the…
A holographic algorithm solves a problem in domain of size $n$, by reducing it to counting perfect matchings in planar graphs. It may simulate a $n$-value variable by a bunch of $t$ matchgate bits, which has $2^t$ values. The transformation…
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…
The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It…
Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic…
Causal holographic information [1] is a variant of the Ryu-Takayanagi proposal for the entanglement entropy of a spatial region in the context of AdS/CFT, but with the bulk surface defined by causality rather than extremality. We…
I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the…
Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…
Holographic algorithms with matchgates are a novel approach to design polynomial time computation. It uses Kasteleyn's algorithm for perfect matchings, and more importantly a holographic reduction . The two fundamental parameters of a…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a…
We prove a singular version of the Engel theorem. We prove a normal form theorem for germs of holomorphic singular Engel systems with good conditions on its singular set. As an application, we prove that there exists an integral analytic…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…