Tunable Superconducting Qubits with Flux-Independent Coherence

We study the impact of low-frequency magnetic flux noise upon superconducting transmon qubits with various levels of tunability. We find that qubits with weaker tunability exhibit dephasing that is less sensitive to flux noise. This insight is used to fabricate qubits where dephasing due to flux noise is suppressed below other dephasing sources, leading to flux-independent dephasing times $T_2^{*}\sim 15\mu \mathrm{s}$ over a tunable range of approximately 340 MHz. Such tunable qubits have the potential to create high-fidelity, fault-tolerant qubit gates and to fundamentally improve scalability for a quantum processor.

Figure 1

Optical micrographs of samples including higher magnification images of qubits and SQUID loops. The sample-B image is a chip of identical design to the one used for our measurements. In the sample-B image, labels indicate each qubit and its individual readout resonators, while unlabeled resonators are bus resonators.

Figure 2

$f_{01}$ vs flux measured for qubits from samples A and B. Solid lines are fits to these tuning curves based on Eq. (1). Also included are frequencies of single-junction qubits from both samples. The dashed lines for these qubits serve as a guide for the eye. (Inset) The entire tuning range measured for the $\alpha =1$ qubit, with the $\alpha =7$ qubit included as a comparison to illustrate the large frequency tunability of an $\alpha =1$ qubit.

Figure 3

${\mathrm{\Gamma }}_{\varphi }$ vs flux measured for qubits from samples A and B. Solid lines show a simultaneous fit of the form $m{D}_{\mathrm{\Phi }}+b$ to the tunable qubits in sample A. Factor $m$ is common to all three data sets, while $b$ is allowed to vary for each. ${\mathrm{\Gamma }}_{\varphi }$, measured for fixed-frequency qubits in both samples, is included with dashed lines as a guide for the eye.

Figure 4

(a) ${\mathrm{\Gamma }}_{\varphi }$ vs $D_{\mathrm{\Phi }}$ measured for qubits from samples A and B. Solid lines show individual linear fits to the tunable qubits in sample A, as described in the text. Note that the scale is log log. ${\mathrm{\Gamma }}_{\varphi }$, measured for fixed-frequency qubits in both samples, is included with dashed lines as a guide for the eye. (b) $T_2^{*}$ vs frequency measured for the $\alpha =15$ and fixed-frequency qubits in sample B.

Figure 5

$T_1$ vs frequency measured for all qubits discussed in the main text. Single points included for $T_1$ values measured for the fixed-frequency qubits.

Figure 6

$T_2^{*}$ vs flux measured for the qubits discussed in the main text. The $T_2^{*}$ values measured for the fixed-frequency qubits in both samples are included with dashed lines as a guide for the eye.

Figure 7

Dependence of $T_1$ with flux for asymmetric transmons, calculated for the asymmetries discussed in the main text, due to coupling to an external flux bias following the analysis of Koch et al. [26]. Although, in our experiments, the symmetric qubit has the value $\alpha =1$, in this calculation, $\alpha =1.1$ is used so that $T_1$ does not diverge at $\mathrm{\Phi }=0$.

Figure 8

Ramsey decay envelopes measured for the $\alpha =1$ qubit at (a) the sweet spot $\mathrm{\Phi }=0$ and (b) $\mathrm{\Phi }=0.3{\mathrm{\Phi }}_0$, where $D_{\mathrm{\Phi }}$ is the largest value measured for this qubit. At each flux point, the Ramsey decay envelopes are fit with both (I) a purely exponential and (II) a Gaussian fit form. Functions fitted to the measured data (the blue open circles) plotted as solid red lines.

Figure 9

$\gamma$ vs flux extracted from fits to the Ramsey measurements on the $\alpha =1$ qubit using Eq. (d2).

Figure 10

$\gamma$ vs $D_{\mathrm{\Phi }}$ extracted from fits to the Ramsey measurements on the $\alpha =1$ qubit using Eq. (d2). The dashed lines are included to indicate the maximum $D_{\mathrm{\Phi }}$ value reached by the $\alpha =7$ (black dashed line) and $\alpha =4$ (blue dotted-dashed line) qubits measured in sample A.

Figure 11

${\mathrm{\Gamma }}_{\varphi }$ vs $D_{\mathrm{\Phi }}$ calculated for the $\alpha =1$ qubit using the exponential, Gaussian [Eq. (d1)], $\gamma$-exponent [Eq. (d2)], and composite [Eq. (d3)] fitting forms.