Related papers: Emergent Braided Matter of Quantum Geometry
The ribbon cocycle invariant is defined by means of a partition function using ternary cohomology of self-distributive structures (TSD) and colorings of ribbon diagrams of a framed link, following the same paradigm introduced by Carter,…
We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of…
In the traditional formalism of quantum mechanics, a simple direct proof of (a version of) the Spin Geometry Theorem of Penrose is given; and the structure of a model of the `space of the quantum directions', defined in terms of elementary…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
The finite strain theory is reformulated in the frame of the Tangential Differential Calculus (TDC) resulting in a unification in a threefold sense. Firstly, ropes, membranes and three-dimensional continua are treated with one set of…
Braid theories are applied to quantum computation processes, where to each crossing in the Braid diagram a unitary Yang-Baxter operator R is associated, representing either a Braiding matrix or a universal quantum gate. By operating with…
The role of quantum groups and braid groups in the description of Standard Model particles is discussed. Some recent results on the use of the quantum group $SU_q(3)$ as a flavour symmetry are reviewed and a connection between two…
An enhanced trivalent tangle is a trivalent tangle with some of its edges labeled. We use enhanced trivalent tangles and classical knot theory to provide a recipe for constructing invariants for trivalent tangles, and in particular, for…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training…
We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group H by an abelian group, with 3-cocycle inflated from a 3-cocycle on H. We also prove that…
We digitally simulate quantum many-body dynamics in emergent curved backgrounds using 80 superconducting qubits on IBM Heron processors. By engineering spatially varying couplings in the spin-$\frac12$ XXZ chain, consistent with the…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…