Semiconductor-Nanowire-Based Superconducting Qubit

We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device (“gatemon”) is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times ($\sim 0.8\mu \mathrm{s}$) and dephasing times ($\sim 1\mu \mathrm{s}$), exceeding gate operation times by 2 orders of magnitude, in these first-generation devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces cross talk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.

Figure 1

InAs nanowire-based superconducting transmon qubit. (a) Scanning electron micrograph of the InAs-Al JJ. A segment of the epitaxial Al shell is etched to create a semiconducting weak link. Inset shows a transmission electron micrograph of the epitaxial $\mathrm{InAs}/\mathrm{Al}$ interface. (b)–(c) Optical micrographs of the completed gatemon device. The nanowire JJ is shunted by the capacitance of the $\mathsf{T}$-shaped island to the surrounding ground plane. The center pin of the coupled transmission line cavity is indicated in (c). (d) Schematic of the readout and control circuit.

Figure 2

Strong coupling of the gatemon to the microwave cavity. (a) Cavity transmission as a function of the cavity drive frequency and $V_G$. The solid blue line shows the bare cavity resonance frequency $f_C$, while the solid green line indicates the gate-voltage dependent qubit frequency $f_Q(V_G)$ extracted from the data. (b) Cavity transmission as a function of the cavity drive at the position indicated by the purple arrows in (a). (c) Frequency splitting between the hybridized qubit-cavity states, $\delta$, as a function of $f_Q$, as extracted from (a). From fitting the solid theory curve we extract the qubit-cavity coupling strength, $g/2\pi =99\mathrm{MHz}$. (d) Parametric plot of the data from (a) as a function of the cavity drive and qubit frequency $f_Q$.

Figure 3

Gatemon spectroscopy and coherent control. (a) The qubit resonance frequency as a function of gate voltage $V_G$ is observed as a distinct feature. (b) Coherent Rabi oscillations are performed at point b in (a) ($V_G=3.4\mathrm{V}$) by applying microwave pulse for time $\tau$ to drive the qubit followed by a readout microwave pulse to probe the cavity response. The main panel shows coherent qubit oscillations as a function of driving frequency and $\tau$. The lower panel shows coherent oscillations at the qubit resonant frequency, corresponding to rotations about the $X$ axis of the Bloch sphere. (c) Coherent oscillations about the $Z$ axis of the Bloch sphere are performed at point c in (a) ($V_G=3.27\mathrm{V}$) by applying a gate voltage pulse $\mathrm{\Delta }{V}_G$ to detune the qubit resonance frequency for time $\tau$. A 15 ns $R_X^{\pi /2}$ microwave pulse is first applied to rotate the qubit into the $X\text{−}Y$ plane of the Bloch sphere and, following the gate pulse, a second $R_X^{\pi /2}$ microwave pulse is used to rotate the qubit out of the $X\text{−}Y$ plane for readout. The main panel shows coherent $Z$ rotations as a function of $\mathrm{\Delta }{V}_G$ and $\tau$. The main panel inset shows the simulated qubit evolution based on $\mathrm{\Delta }{f}_Q(V_G)$ extracted from (a). The lower panel shows coherent $Z$ oscillations as a function of $\tau$ for $\mathrm{\Delta }{V}_G=20.9\mathrm{mV}$. In both (b) and (c) the demodulated cavity response $V_H$ is converted to a normalized qubit state probability $p_{|1⟩}$ by fitting $X$ rotations to a damped sinusoid of the form $V_H^0+\mathrm{\Delta }{V}_H\exp (-\tau /T_{\text{Rabi}})\sin (\omega \tau +\theta )$ to give $p_{|1⟩}=(V_H-V_H^0)/2\mathrm{\Delta }{V}_H+1/2$. The solid curves in the lower panels of (b) and (c) are also fits to exponentially damped sine functions.

Figure 4

Gatemon quantum coherence. (a) Left panel shows a lifetime measurement for sample 1 at point b in Fig. 3 ($V_G=3.4\mathrm{V}$). A 30 ns $R_X^{\pi }$ pulse excites the qubit to the $|1⟩$ state and we vary the wait time $\tau$ before readout. The solid line is a fit to an exponential curve. The right panel shows a Ramsey experiment used to determine $T_2^{*}$ for sample 1 with the wait time, $\tau$, between two slightly detuned 15 ns $R_X^{\pi /2}$ pulses varied before readout. The solid curve is a fit to an exponentially damped sinusoid. (b) We repeat the lifetime and Ramsey experiments as in (a) for sample 2 with $f_Q=4.426\mathrm{GHz}$ ($V_G=-11.3\mathrm{V}$). In red, we perform a Hahn echo experiment by inserting an $R_X^{\pi }$ pulse between two $R_X^{\pi /2}$ pulses. The decay envelope is measured by varying the phase $\varphi$ of the second $\pi /2$ microwave pulse and extracting the amplitude of the oscillations. The solid red line is a fit to an exponential curve.