Related papers: Complexity measures from geometric actions on Vira…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was…
This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups $G$ with central extensions, with gauge group $H$…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
We study the symmetry group properties of the variable coefficient Davey-Stewartson (vcDS) system. The Lie point symmetry algebra with a Kac-Moody-Virasoro (KMV) structure is shown to be isomorphic to that of the usual (constant…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion…
We explore $T \overline T$ deformations of Warped Conformal Field Theories (WCFTs) in two dimensions as examples of $T\overline T$ deformed non-relativistic quantum field theories. WCFTs are quantum field theories with a…
We study the crossing symmetry of the ensemble of large-$c$ 2D CFTs defined through 3D gravity. A central observation is that statistical moments of OPE coefficients are not independent; rather, lower and higher moments are strongly…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…
The study of subshifts on groups different from $\mathbb{Z}$, such as $\mathbb{Z}^d$, $d\geq 2$, has been a subject of intense research in recent years. These investigations have unveiled aremarkable connection between dynamics and…
We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach is more adequate for the analysis of an impact of symmetry on the the motion…
This paper provides a zeroth-order optimisation framework for non-smooth and possibly non-convex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure…
We revisit the critical two-dimensional Ashkin-Teller model, i.e. the $\mathbb{Z}_2$ orbifold of the compactified free boson CFT at $c=1$. We solve the model on the plane by computing its three-point structure constants and proving crossing…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
The path integral of pure 3D gravity with negative cosmological constant is formulated on a finite region of spacetime $M$, with boundary conditions that fix geodesic lengths or dihedral angles on $\partial M$. In the dual CFT, this…
We present a set of noncommuting frame-translation symmetries in 4D gravity in tetrad-connection variables, which allow expressing diffeomorphisms as composite transformations. Working on the phase space level for finite regions, we pay…
We study the emergence of two-dimensional conformal symmetry in critical quantum spin chains on the finite circle. Our goal is to characterize the conformal field theory (CFT) describing the universality class of the corresponding quantum…