Observation of High Coherence in Josephson Junction Qubits Measured in a Three-Dimensional Circuit QED Architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with $T_2\sim 10$ to $20\mu \mathrm{s}$ without the use of spin echo, and highly stable, showing no evidence for $1/f$ critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few ${10}^{-4}$, approaching the error correction threshold.

Figure 1

Qubit coupled to a 3D cavity. (a) Schematic of a transmon qubit inside a 3D cavity. The qubit is coupled to the cavity through a broadband dipole antenna that is used to receive and emit photons. (b) Photograph of a half of the 3D aluminum waveguide cavity. An aluminum transmon qubit with the dipole antenna is fabricated on a $c$-plane sapphire substrate and is mounted at the center of the cavity. (Inset) Optical microscope image of a single-junction transmon qubit. The dipole antenna is 1 mm long. (c) Transmission of a 3D cavity (cavity D) coupled to a transmon ($J1$) measured as a function of power and frequency. The cavity response above $-80\mathrm{dBm}$ occurs at the bare cavity frequency $f_c=8.003\mathrm{GHz}$. At lower powers, the cavity frequency shifts by $g^2/\delta$.

Figure 2

Time-domain measurement of the qubit coherence (a) Relaxation from $|1⟩$ of qubit $J1$. $T_1$ is $60\mu \mathrm{s}$ for this measurement. (Inset) The pulse sequences used to measure relaxation (upper) and Ramsey experiments with and without echo (lower). The pulse shown in dashed line is an echo signal applied at one half of the delay between two $\pi /2$ pulses. (b) Ramsey fringes measured on resonance with (blue squares online or upper curve) and without (red squares online or lower curve) echo sequence. The pulse width for the $\pi$ and $\pi /2$ pulses used in the experiments is 20 ns. An additional phase is added to the rotation axis of the second $\pi /2$ pulse for each delay to give the oscillatory feature to the Ramsey fringes. (c) Qubit frequency $f_{01}$ measured over 23 h by repeated Ramsey measurements.

Figure 3

Temperature dependence of qubit properties. (a) Measurement of $T_1$, $T_{\mathrm{echo}}$, and $T_2$. (b) Shift of the transition frequency $f_{01}$. Black dashed curves in (a) and (b) are theoretical $T_1$ and $f_{01}$ calculated from the model in Ref. 26 plus a temperature-independent relaxation rate with the same fitting parameter of $\Delta =194\mu \mathrm{eV}$ for both $T_1$ and $f_{01}$. (See Supplemental Material [22] for details.) The blue small-dashed curve is the theoretical $T_2$ from $1/f$ critical current fluctuations predicted by Ref. 23.