Implementation of single-qubit gates via parametric modulation in the Majorana transmon

Abstract

We present a voltage gate-based method for controlling the Majorana transmon, using a sinusoidal modulation of the induced offset charge $n_g$. Working in the transmon regime and in the instantaneous eigenstates basis, we find the time evolution under this protocol that realises tunable $X$-$Z$ rotations. We optimise the parameters of the system for different single-qubit gates in both the laboratory frame and the qubit rotating frame, obtaining qubit control errors $1-\mathcal{F}$ smaller than $\sim 2\times 10^{-4}$. In addition to this, we conduct an analysis of the effects of the charge noise, assuming wide-band $1/f$ additive noise in $n_g$, both for the free and the driven evolutions. For the free evolution, the relaxation and dephasing rates are calculated perturbatively, obtaining long dephasing times of the order of milliseconds at the system's sweet-spots. For the driven case, the average fidelity for the $X$-gate is obtained via a numerical simulation, demonstrating remarkable resilience.

References in corpus (17)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Charge insensitive qubit design derived from the Cooper pair box
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Electrically detected interferometry of Majorana fermions in a topological insulator
• Scaling of Majorana Zero-Bias Conductance Peaks
• Decoherence benchmarking of superconducting qubits
• Majorana box qubits
• Low-decoherence flux qubit
• Thermal and Residual Excited-State Population in a 3D Transmon Qubit
• Dephasing of solid-state qubits at optimal points
• Influence of Topological Edge States on the Properties of Al/Bi2Se3/Al Hybrid Josephson Devices
• Readout of Majorana Qubits
• Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
• Parity-to-charge conversion in Majorana qubit readout
• Microwave readout of Majorana qubits

Cited by in corpus (1)

• Electromagnetic response of the surface states of a topological insulator nanowire embedded within a resonator