Related papers: Topological phases and quantum computation
We study a one-dimensional topological superconductor, the Kitaev chain, under the influence of a non-Hermitian but $\mathcal{PT}$-symmetric potential. This potential introduces gain and loss in the system in equal parts. We show that the…
While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on…
One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by…
The Kitaev honeycomb model, which is exactly solvable by virtue of an extensive number of conserved quantities, supports a gapless quantum spin liquid phase as well as gapped descendants relevant for fault-tolerant quantum computation. We…
These are lecture notes of the QFT-I course I gave in an online mode at Chennai Mathematical Institute. The course focussed on the free relativistic quantum fields, their interactions in the perturbative scattering framework, standard…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev's toric code in a field. This demands to include the non-local effects mediated by…
We define an exactly solvable model for 2+1D topological phases of matter on a triangulated surface derived from a crossed module of semisimple finite-dimensional Hopf algebras, the `Hopf-algebraic higher Kitaev model'. This model…
The 2D toric code is a prototypical example that exhibits non-trivial topological properties and a ground state possessing a non-trivial topological order. Until now, all the cases studied in the literature have been in the stable…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
This report describes my experience teaching a graduate-level quantum computing course at Northeastern University in the academic year 2022-23. The course takes a practical, software-driven approach to the course, teaching basic quantum…
Hystory of topology is discussed uncluding the Golden Age Period (1950-1970), the Period of Decay (1970-1980) and the Period of Recovery in 80s and 90s based on the ideas borrowed from physics community. In the second part recent result of…
These are lecture notes based on a series of lectures presented at the XIII Modave Summer School in Mathematical physics aimed at PhD students and young postdocs. The goal is to give an introduction to some of the recent developments in…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…