Related papers: Complexity of quantum cohomology
We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory and 3d Riemannian quantum gravity, whose dynamical variables are flat discrete connections with compact structure…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted…
We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives a new geometric point of view on these…
Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one…
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated…
This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Let $(V,Z)$ be a Topological Quantum Field Theory over a field $f$ defined on a cobordism category whose morphisms are oriented $n+1$-manifolds perhaps with extra structure. Let $(M,\chi)$ be a closed oriented $n+1$-manifold $M$ with this…
One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
We compute the cohomology of polygon spaces using their identification to (semi) stable configuration of weighted points on complex projective line. This cohomology is already given by J.C.Hausmann and A. Knutson but we use a different…
The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…
John C.Baez reinterpreted 2-dimensional and 3-dimensional topological quantum field theories (abbreviated as 2-TQFT and 3-TQFT) in "A prehistory of n-categorical physics"[JC11]. Inspired by his idea, this paper utilizes cochains to prove…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
We construct the TQFT on symplectic cohomology and wrapped Floer cohomology, possibly twisted by a local system of coefficients, and prove that the TQFT respects Viterbo restriction maps and the canonical maps from ordinary cohomology. We…
The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is simply connected at infinity as we done…
Given a closed monotone symplectic manifold $M$, we define certain characteristic cohomology classes of the free loop space $L \text {Ham}(M, \omega)$ with values in $QH_* (M)$, and their $S^1$ equivariant version. These classes generalize…