Related papers: Photonic implementation of Majorana-based Berry ph…
In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Majorana Fermions) is very important, really exotic, and completely robust. The race for searching Majorana zero modes and verifying the corresponding…
$\pi/8$ phase gates (magic gates or T-gates) are crucial to augment topological systems based on Majorana zero modes to full quantum universality. We present a scheme based on a combination of projective measurements and non-adiabatic…
Majorana fermions are the real (in a mathematical sense) counterparts of complex fermions like ordinary electrons. The promise of topological quantum computing has lead to substantial experimental progress in realizing these particles in…
Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key…
The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
By studying the topological invariance andBerry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance for non-Hermitian…
Jones polynomials were introduced as a tool to distinguish between topologically different links. Recently, they emerged as the central building block of topological quantum computation: by braiding non-Abelian anyons it is possible to…
A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states…
Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate…
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution…
Phases arising from cyclic processes are fundamental in physics, bridging quantum and classical domains and providing deeper insights into the topology and dynamics of physical systems. This study investigates the accumulation of a…
Qubits in topological quantum computation are built from non-Abelian anyons. Adiabatic braiding of anyons is exploited as topologically protected logical gate operations. Thus, the adiabaticity upon which the notion of quantum statistics is…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
Non-Abelian geometric phases form the foundation of fault-tolerant holonomic quantum computation. An "all-geometric" approach leveraging these phases enables robust unitary operations in condensed matter systems. Photonics, with rich…
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…
Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by…
The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very…
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…
Majorana fermions subject to the non-Abelian braid group are believed to be the basic ingredients of future topological quantum computations. In this work, we propose to simulate Majorana fermions of the Kitaev model in electric circuits…