Related papers: A topological quantum field theory approach to gra…
Here we observe that list coloring in graph theory coincides with the zero-temperature antiferromagnetic Potts model with an external field. We give a list coloring polynomial that equals the partition function in this case. This is…
We define a family of quantum invariants of closed oriented $3$-manifolds using spherical multi-fusion categories. The state sum nature of this invariant leads directly to $(2+1)$-dimensional topological quantum field theories…
Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological…
Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs…
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind,…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a "quantum-classical game"--that is, a non-local game of two…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs.…
We study the virtual Euler characteristics of sheaves over Quot schemes of curves, establishing that these invariants fit into a topological quantum field theory (TQFT) valued in $\mathbb{Z}[[q]]$. We show that the three-pointed genus-zero…
Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots and links, tangles impose more relaxed constraints,…
We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…
We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging $G$-equivariant invertible spin-TQFTs, or, in physics language,…
We investigate topological invariants in strongly interacting many-body systems within holographic mean-field theory (H-MFT) framework. Analytic expressions for retarded Green's functions are obtained for all possible fermionic bilinear…
Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime…
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…