High-Coherence Hybrid Superconducting Qubit

We report quantum coherence measurements of a superconducting qubit whose design is a hybrid of several existing types. Excellent coherence times are found: $T_2^{*}\sim T_1\sim 1.5\mu \mathrm{s}$. The topology of the qubit is that of a traditional three-junction flux qubit, but it has a large shunting capacitance, and the ratio of the junction critical currents is chosen so that the qubit potential has a single-well form. The qubit has a sizable nonlinearity, but its sign is reversed compared with most other popular qubit designs. The qubit is read out dispersively using a high-$Q$ resonator in a $\lambda /2$ configuration.

Figure 1

Micrograph and simulated frequency response of the low-$Z$ flux qubit. (a) A micrograph of the qubit shows the interdigitated shunting capacitor ($C_s=100\mathrm{fF}$), which is made of aluminum simultaneously with the junction fabrication step. The qubit has three junctions, as in the traditional flux qubit. (b) The qubit frequency response is much weaker than the traditional flux qubit (inset: derivative $\partial f_{01}/\partial {\Phi }_0$). Near the sweet spot at $\Phi =0.5{\Phi }_0$ the qubit anharmonicity is inverted: ${\omega }_{12}>{\omega }_{01}$. Simulation parameters are $C_s=100\mathrm{fF}$, $I_0=0.3\mu \mathrm{A}$, and $\alpha =0.3$. (d) The qubit is read out dispersively by coupling it capacitively via $C_{\mathrm{qr}}\sim 1.6\mathrm{fF}$ to a half-wavelength coplanar waveguide resonator with a resonance frequency of $f_r=10.35\mathrm{GHz}$.

Figure 2

Experimental setup. (a) The resonator is capacitively coupled to a feed line. Both the microwaves and dc bias are inductively coupled to the qubit. (b) The qubit is measured dispersively using standard microwave techniques (e.g., 7). (c) The qubit is mounted on a copper PC board with a high frequency miniature SMA connector. The dc flux bias is generated using a hand-wound external superconducting wire coil mounted on the lid of the box. The microwave bias is supplied by a microwave wire bond on chip that has a small mutual inductance to the qubit loop.

Figure 3

Qubit spectroscopy. (a) The vacuum-Rabi splitting indicates $g=45\mathrm{MHz}$. (b) Qubit spectroscopy over a broad flux range agrees well with the one-dimensional theory (dashed line). Because the raw data shows a spectroscopic linewidth of a few MHz it would not be visible on this scale and therefore the data were significantly broadened in software by averaging over 40 MHz to make it visible on this plot. A box mode near 5.6 GHz couples microwaves much more strongly to the qubit than all other frequencies. There is a noticeable offset in flux due to residual magnetic fields in the refrigerator. (c) Qubit spectroscopy near the sweet spot (data not broadened) reminds us of the typical parabolic response of the flux qubit. (d) The two-photon $|0⟩\to |2⟩$ transition is higher in frequency, revealing the inverted anharmonicity of the low-$Z$ flux qubit.

Figure 4

Coherence time measurements of the qubit. (a) Rabi oscillations. Each trace varies in microwave amplitude by a factor of 2, and we find the Rabi frequency scales accurately with amplitude. (b) A direct measure of the energy decay is obtained from a fit to the data (gray dashed line) and is found to be $T_1=1.6\mu \mathrm{s}$. (c) Ramsey fringes are implemented by applying a Hadamard gate (180° rotation around an axis tilted by 45° from the horizontal axis). The detuning between the qubit and microwave frequency is $\sim 10\mathrm{MHz}$, consistent with the observed period. The data can be fitted to an exponential decay with a decay constant $T_2^{*}\sim 1.3\mu \mathrm{s}$.