Related papers: Non-Abelian statistics as a Berry phase in exactly…
We develop a rigorous and highly accurate technique for calculation of the Berry phase in systems with a quadratic Hamiltonian within the context of the Kitaev honeycomb lattice model. The method is based on the recently found solution of…
We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering…
We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between…
Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the…
Many trial wavefunctions for fractional quantum Hall states in a single Landau level are given by functions called conformal blocks, taken from some conformal field theory. Also, wavefunctions for certain paired states of fermions in two…
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…
The variational quantum eigensolver (VQE) is an algorithm to find eigenenergies and eigenstates of systems in quantum chemistry and quantum many-body physics. The VQE is one of the most promising applications of near-term quantum devices to…
The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that…
We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for non-Abelian…
Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction ($\hat{V}^\text{Pf}_3$) between electrons…
In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is…
We propose a scheme to probe the non-Abelian statistics of the collective anyonic excitation in Kitaev's honeycomb model with cold atoms in an optical lattice. The generation of the anyonic excitation can be realized by simple rotating…
The adiabatic theorem is one of the most interesting and significant theorems in quantum mechanics. However, the adiabatic theorem can fail for general non-Hermitian quantum systems. In this paper, by utilizing the complex geometric phase,…
In this work, we study the counterdiabatic driving scheme in pseudo- and antipseudo- Hermitian systems. By discussing the adiabatic condition for non-Hermitian system, we show that the adiabatic evolution of state can only be realized in…
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…
Observation of non-Abelian statistics for the e/4 quasiparticles in the \nu=5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states…
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory. We find…
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…
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…
In a nondegenerate syste, the abelian Berry's phase will never cause transitions among the Hamiltonian's eigenstate. However, in a degenerate syatem, it is well known that the state transition can be caused by the non-abelian Berry phase.…