Manipulating the Majorana qubit with Landau-Zener-Stückelberg interference

Abstract

Constructing a universal operation scheme for Majorana qubits remains a central issue for the topological quantum computation. We study the Landau-Zener-Stückelberg interference in a Majorana qubit and show that this interference can be used to achieve controllable operations. The Majorana qubit consists of an rf SQUID with a topological nanowire Josephson junction which hosts Majorana bound states. In the SQUID, a magnetic flux pulse can drive the quantum evolution of the Majorana qubit. The qubit experiences two Landau-Zener transitions when the amplitude of the pulse is tuned around the superconducting flux quanta 2e/ . The Landau-Zener-Stückelberg interference between the two transitions rotates the Majorana qubit, with the angle controlled by the time scale of the pulse. This rotation operation implements a high-speed single-qubit gate on the Majorana qubit, which is a necessary ingredient for the topological quantum computation.

Landau-Zener-Stückelberg Interferometry for Majorana Qubit

“…At sufficiently low temperatures, currents flowing into and from the nanowires are carried by Cooper pairs, which preserves the total parity of the system. Therefore, the low-energy physics is described by the following Hamiltonian 39 , 40 , with basis of the even- and odd-parity state , where τ x,z are Pauli matrices and is the phase difference between the two superconductors which can be driven dynamically by a bias voltage across the junction. The interaction term δ between the two parity states is determined by couplings between MQs in individual 1D topological superconductors by [ δ L between γ 1 and γ 2 and δ R between γ 3 and γ 4 as shown in Fig.…”

Josephson radiation patterns in underdamped topological Josephson junctions

“…Recent experimental efforts are concentrated on studying dynamical properties such as electromagnetic radiation from the junction [14][15][16] . This Josephson radiation was predicted by standard resistively shunted junction model to have a series of spectra with frequencies f = neV /h 17,18 , where the first one f M = eV /h corresponds to the 4π-period Josephson effect and the second one f J = 2eV /h corresponds to conventional 2π-period Josephson effect 12,[19][20][21] . Several recent experiments successfully observed the 4π-period Josephson radiation with frequency f M , but its relation to the Majorana zero modes are still under debate because the signals lacks smoking gun features to be determined uniquely from Majorana zero modes 12,20,22 .…”

“…Hybridization of Majorana zero modes leads to a quantum two-level system 6 , with its Hamiltonian determined by the Josephson phase. We have included this Majorana two-level system into the standard theory, and built a quantum resistively and capacitively shunted junction model to study the dynamics of the topological Josephson junction 10,18,[23][24][25] . Inspired by recent experiments, we perform frequency analysis within this model and calculate the Josephson radiation.…”

Josephson and Persistent Currents in a Quantum Ring between Topological Superconductors

“…Since Weyl points in crystals require the breaking of or inversion symmetry, in four‐terminal junctions, the Weyl and nodal points may also occur under symmetry. [ 30–32 ] The importance of the Josephson junctions lies in the engineering of Andreev bound states (ABSs) and their control by building topological quantum‐computing architectures based on MBSs, [ 33–37 ] where superconducting phase difference, bias voltage, and magnetic flux play the role of control parameters. [ 38,39 ] To observe MBSs in 1D topological superconductors (TSCs), one of the most suggested models is based on quantum dots (QDs) because they are easily tunnelable objects.…”