In quantum mechanics, the spaces of momentum and its conjugate, the position, are related via Fourier transforms and thus the properties are interwoven with their structure. In particular, for lattice systems possessing an underlying discrete position space, the momentum becomes finite. Moreover, if the lattice length is finite, $L<\infty$, the momentum space also becomes both finite and discrete breaking altogether the continuity of the dispersion relation. This aspect is relevant in new systems such as the topological materials. We address this point paving the path for new ways to the observation of Majorana quasi-particles. Furthermore, the Kitaev model, which is the simplest Hamiltonian supporting Majorana fermions, is therefore taken as a starting point for the theoretical description of the work. Our study focuses on finding the zero-energy modes in an artificial arrangement of a non-interacting superconducting finite nanowire by using a discrete-sine transform with the purpose of going from position to momentum space considering hard-wall boundary conditions in the process. Here, a new $L$-dimensional Nambu operator to diagonalize the system in the Bogoliubov-de Gennes formalism is proposed and, further, we arrive to a new space with a considerable reduced dimension allowing the treatment of larger system sizes.
We also present a comparison between the numerical and third order perturbation theory for the weak coupling regime results presenting an excellent agreement. Finally, we analyze the wavefunctions of the retrieved zero-energy modes showing that they are indeed edge states and thus they have an exponential decay.
The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key fe…
Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of …
Topological stability is an important property for topological materials. However, the non-Hermitian effects may change this situation. Here, we investigate the robustness of edge states in the non-Hermitian Kitaev chain with imbalanced tunneling term and superconducting pairing term. By defining the similarity of Majorana zero modes (MZMs) and magnetic factor, the coalescing phase diagram of the MZMs and corresponding spin polarization phase diagram are provided. Because of the non-Hermitian coalescence effect and non-Hermitian suppression effect induced by the breakdown of sublattice symmetr…
Majorana parity qubit in coupled minimal Kitaev chains
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克研究所和卡弗里纳米科学研究所）；Department of Applied Physics, Eindhoven University of Technology（埃因霍温理工大学应用物理系）
We study a Kitaev model on a square lattice, which describes topologically trivial superconductor when gap opens, while supports topological gapless phase when gap closes. The degeneracy points are characterized by two vortices in momentum space, with opposite winding numbers, which are not removable unless meet together. We show rigorously that the topological gapless phase always hosts a partial Majorana flat band edge modes in a ribbon geometry, although such a single band model has zero Chern number as a topologically trivial superconductor. The flat band disappears when the gapless phase …
Majorana bound states in a hybrid Kitaev ladder with long-range pairing
Indian Institute of Technology (Banaras Hindu University)（印度技术学院（贝拿勒斯印度教大学））；National Institute of Science Education and Research（国家科学教育与研究研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Rzeszow University of Technology（热舒夫理工大学）
Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wavefunctions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static ("0+0D") large-$N$ field theory to study the energy, two…
Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version, and realizing the ground states in a superconducting quantum processor. The teleportation tran…
We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here, the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding freque…
We quantitatively study the out-of-equilibrium edge-Majorana correlation in a linearly ramped one-dimensional Kitaev chain of finite length in a dissipative environment. The chemical potential is dynamically ramped to drive the chain from its topologically trivial to nontrivial phase in the presence of couplings to nonthermal Markovian baths. We consider two distinctive situations: In the first situation, the bath is quasilocal in the site basis (local in quasiparticle basis) while in the other it is local. Following a Lindbladian approach, we compute the early time dynamics as well as the asy…
We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets. It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from $\pm 1$ to zero. This gapful spin liquid state with zero Chern number is nothing but the toric code p…
