Related papers: Topological QBits in Flux-Quantized Super-Gravity
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity.…
We construct global solutions to Type IIB supergravity with 16 residual supersymmetries whose space-time is $AdS_6 \times S^2$ warped over a Riemann surface. Families of solutions are labeled by an arbitrary number $L\geq 3$ of asymptotic…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
We explicitly construct a solution of eight-dimensional gauged supergravity representing D6-branes wrapped on six-cycles inside Calabi-Yau fourfolds. The solution preserves two supercharges and asymptotically is a cone with the coset space…
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
For smooth finite dimensional manifolds, we characterise gerbes with connection as functors on a certain surface cobordism category. This allows us to relate gerbes with connection to Turaev's 1+1-dimensional homotopy quantum field…
Over a decade before the modern formulation of AdS/CFT duality, Duff et al. had observed a candidate microscopic explanation by identifying the CFT fields with fluctuations of probe p-branes stretched out in parallel near the horizon of…
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a…
We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The fusion rules induce an association scheme with Krein…
The prospect of coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…
Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations…
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…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…