Two-qubit operation on Majorana qubits in ordinary-qubit chains
Majorana zero modes can be simulated in structures based on spin or quasi-spin degrees of freedom,
e.g., Josephson-qubit chains. Braiding of Majorana degrees of freedom is realized using T -junctions supplied with an auxiliary spin (ancilla). Motivated by prospective experiments, we analyze the braiding in the spin representation, which provides the basis for the analysis of imperfections characteristic to the spin and qubit designs. The result of the braiding operation is straightforwardly found for the initial basis states of the two qubits and the ancilla, up to phase factors. Here we fix these phase factors and thus describe the complete two-qubit operation. This result is relevant for physical simulation of the Majorana qubits in Josephson-qubit chains and other spin or qubit structures.
A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to interaction with the quantized photon mode. One of the channels for this process is the dynamical Lamb effect, induced by a nonadiabatic modulation of the atomic-level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (an artificial macroscopic atom) provides a unique platform for observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying the coupling nonadiabatically, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. The dynamics of such a coupled system is studied within the Rabi model with a time-dependent coupling constant and beyond the rotating-wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of the qubit-resonator coupling energy is proposed. © 2015 American Physical Society. ©2015 American Physical Society.
Methods for controlling states of interacting superconducting flux qubits using power-efficient devices of fast single-quantum logic (Josephson nonlinearity cavities) are studied. One- and two-qubit quantum logical operations performed within the conventional control technique using Rabi pulses and using picosecond single unipolar magnetic field pulses are comparatively analyzed. It is shown that all main operations can be implemented with an accuracy of better than 97% due to optimization of the shape and parameters of unipolar control pulses (associated with, e.g., propagation of fluxons in transmission lines). The efficiency of the developed technique for programming a two-qubit quantum processor implementing the simplest Deutsch–Jozsa algorithm is demonstrated.
The present study is devoted to development of a technique for numerical simulation of the wave function dynamics the single Josephson qubits and arrays of noninteracting qubits controlled by ultra-short pulses. We wish to demonstrate the feasibility of a new principle of basic logical operations on the picosecond timescale. The influence of the unipolar pulse (“fluxon”) form on the evolution of the state during the execution of the quantum onequbit operations – “NOT”, “READ” and “ SQR-NOT” – is investigated in the presence of decoherence. In the array of non interacting qubits, the question of the influence of the spread of their energy parameters (tunnel constants) is studied. It is shown that a single unipolar pulse can control a huge array of artificial atoms with 10% spread of geometric parameters in the array.
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.
Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.