Related papers: Complexity of quantum cohomology
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
The statistical complexity of continuous-variable quantum states can be characterized with a quantifier defined in terms of information-theoretic quantities derived from the Husimi Q-function. In this work, we utilize this complexity…
We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a…
Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute the…
In previous work, we proposed a general framework of positive topological field theories (TFTs) based on Eilenberg's notion of summation completeness for semirings. In the present paper, we apply this framework in constructing explicitly a…
In this article, we investigate the higher topological complexity of oriented Seifert fibered manifolds that are Eilenberg--MacLane spaces $K(G,1)$ with infinite fundamental group $G$. We first refine the cohomological lower bounds for…
An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the…
C. A. Fuchs and M. Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is closely related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs…
We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group $G$. It has been conjectured that such states are classified by the cohomology group $H^3(G,U(1))$, but the completeness of this…
We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are…
We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of an arbitrary $d$-dimensional smooth projective toric manifold ${\bf P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of $H^*_{\varphi}({\bf…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent…
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The…
We determine topological complexity of a series of finite spaces which is weakly homotopy equivalent to a circle $S^1$, and give a finite space $X$ satisfying the inequality tc$(X) <$ cat$(X {\times} X)$. This answers two conjectures on…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 24 inflection points on quartic curves. In particular, we…
A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological…
On a symplectic manifold $M$, the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let $\hbar$ denote the parameter. Associated to them is the quantum $\mathcal{D}$ -…