Parity-Protected Superconductor-Semiconductor Qubit

Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a $\cos (2\phi )$ Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

Figure 1

Qubit circuit and device design. (a) Circuit schematic of the parity-protected qubit formed from high-transparency few-channel semiconductor Josephson junctions in a flux-biased interferometer shunted by a large capacitor (blue). (b),(c) Energy-phase relation of the interferometer for (b) different junction transmission coefficients and (c) junction asymmetries. (d) False-color optical micrograph of the device showing the large island (blue) that forms one side of the shunting capacitor. (e),(f) False-color electron micrographs of the nanowire junctions. (f) A small segment of the Al shell on an InAs nanowire is etched away to form a semiconductor Josephson junction. A nearby electrostatic gate (red) allows for the tuning of the electron density in the junction.

Figure 2

Qubit spectroscopy as a function of applied flux ($V_1=1.4\mathrm{V}$ and $V_2=-0.445\mathrm{V}$). (a) Frequency of the readout cavity as the qubit spectrum is tuned with flux. Solid and dashed lines indicate crossings of qubit transition frequencies as determined from fits to the data in (c). (b) Two-tone spectroscopy of the qubit transition frequencies. An average of each column has been subtracted. (c) Extracted transition frequencies from (b) with solid lines a fit to Eq. (2). Diagrams above illustrate the fitted potential for different values of $\mathrm{\Phi }$. Gray dashed lines indicate multiphoton transitions due to the simultaneous drive and readout tones.

Figure 3

Voltage control of potential barrier. (a) Gate voltages are tuned to a balanced regime with the two junctions of similar value ($V_1=1.2\mathrm{V}$ and $V_2=-0.12\mathrm{V}$). (b) Qubit potential (solid black line) and wave functions for the two lowest energy states extracted from a fit to data in (a) at $\mathrm{\Phi }={\mathrm{\Phi }}_0/2$. (c) The charge distribution of the two lowest energy states. (d) Gate voltages tuned to an unbalanced regime with one junction much smaller than the other ($V_1=1.241\mathrm{V}$ and $V_2=-0.386\mathrm{V}$). (e) Qubit potential and wave functions for the two lowest energy states extracted from fits to (d). (f) The charge distribution of the two states.

Figure 4

Coherent control. Rabi oscillations in (a) the transmon regime with $\mathrm{\Phi }=0$ and $f_{\text{Drive}}=7.911\mathrm{GHz}$ and (b) a tilted $\pi$ qubit regime with $\mathrm{\Phi }=0.512{\mathrm{\Phi }}_0$ and $f_{\text{Drive}}=5.725\mathrm{GHz}$. Diagrams show the qubit potentials and lowest energy states. Voltages are fixed at $V_1=-1.25\mathrm{V}$ and $V_2=-0.445\mathrm{V}$ for both (a) and (b). The solid line in (a) is a fit to an exponentially decaying sinusoidal function, while in (b) the fit function has an additional exponentially decaying offset (black line).

Figure 5

Lifetime measurements in the transmon regime with $\mathrm{\Phi }=0$ and $f_{\text{Drive}}=7.911\mathrm{GHz}$ (blue) and the tilted potential regime with $\mathrm{\Phi }=0.512{\mathrm{\Phi }}_0$ and $f_{\text{Drive}}=5.725\mathrm{GHz}$ (red). Blue solid line is an exponential fit. Red dashed line is a double exponential fit $A_1{e}^{-\tau /T_1^{|1⟩}}+A_2{e}^{-\tau /T_1^{|2⟩}}$ with the solid line showing $A_1{e}^{-\tau /T_1^{|1⟩}}$ (see main text). Data are normalized to fit parameters.