Related papers: Knot Logic and Topological Quantum Computing with …
Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible…
Quantum devices may overcome limitations of classical computers in studies of nuclear structure functions and parton Wigner distributions of protons and nuclei. In this talk, we discuss a worldline approach to compute nuclear structure…
Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial…
The list of quantum mechanical systems with non-Abelian statistics has recently been expanded by including generic spin-orbit-coupled semiconductors e.g., InAs) in proximity to a s-wave superconductor. Demonstration of the anyonic…
We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyon. This knot lattice model bears abelian and non-abelian anyons as well as integral and fractional filling states that is similar to quantum Hall…
We review the q-deformed spin network approach to topological quantum field theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the…
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…
We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted external magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor…
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional…
Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot tunnel-coupled to two topological superconductors.…
Quantum simulation of fermionic systems is a promising application of quantum computers, but in order to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as…
A fundamental obstacle for achieving quantum computation is local decoherence. One way to circumvent this problem rests on the concepts of topological quantum computation using non-local information storage, for example on pairs of Majorana…
For an electrically driven electron confined in a nanowire quantum dot with spin-orbit coupling (SOC), we find a SOC-magnetism phase-locked condition under which we derive a complete set of Schr\"odinger kitten states which contains some…
We study the stability of the topological quantum computation proposals involving Majorana fermions against thermal fluctuations. We use a minimal realistic model of a spinless px+ipy superconductor and consider effect of excited midgap…
A quantum knot model of mesons and baryons is established. This quantum knot model is derived from a quantum gauge model which is similar to the QCD gauge model. We first establish a knot model of the $\pi$ mesons. We show that the $\pi$…
Emergent anyons are the key elements of the topological quantum computation and topological quantum memory. We study a two-component fermion model with conventional two-body interaction in an open boundary condition and show that several…
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…
In this article, we propose the realization of conformal manifolds, which are smooth manifolds of scale-conformal invariant interacting Hamiltonians in two-dimensional quantum many-body systems. Such phenomena can occur in various…