Related papers: Photonic implementation of Majorana-based Berry ph…
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
Ettore Majorana, in his short life, unintendedly has uncovered the most profound problem in quantum computation by his discovery of Majorana fermion, a particle which is its own anti-particle. Owing to its non-Abelian exchange statistics,…
Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental…
The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions…
For systems of lattice anyons like Majorana and parafermions, the unconventional quantum statistics determines a set of global symmetries (e.g., fermion parity for Majoranas) admitting no relevant perturbations. Any operator that breaks…
Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states.…
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric…
The evolution of a quantum system is governed by the associated Hamiltonian. A system defined by a parameter-dependent Hamiltonian acquires a geometric phase when adiabatically evolved. Such an adiabatic evolution of a system having…
Quasiparticle poisoning, expected to arise during the measurement of Majorana zero mode state, poses a fundamental problem towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana…
Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with…
The behavior of quantum states at exceptional points and at critical points associated with quantum phase transitions is intriguing yet puzzling. In this study, we present an alternative method for obtaining the Berry potentials using the…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
Recently, it is proposed to do quantum computation through the Berry's phase(adiabatic cyclic geometric phase) shift with NMR (Jones et al, Nature, 403, 869(2000)). This geometric quantum gate is hopefully to be fault tolerant to certain…
A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves…
Given recent progress in the realization of Majorana zero modes in semiconducting nanowires with proximity-induced superconductivity, a crucial next step is to attempt an experimental demonstration of the predicted braiding statistics…
We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
We introduce exactly solvable models of interacting (Majorana) fermions in $d \ge 3$ spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological…