Figure 1

Qubit frequency ${\omega }_{10}/2\pi$ vs current bias for the conventional single-element design (top trace, shifted for clarity) and the capacitively shunted design (bottom trace). The bias current $I_J$ tunes the frequency of the qubit [4, 5]. The density of splittings in the conventional design is high enough that the qubit is almost always coupled to at least one TLS. The state occupation of $|1⟩$ is consequently diminished, giving rise to decoherence and thus reducing qubit performance. The new design has about one tenth of the area and consequently exhibits a reduction in the number of avoided level crossings by approximately a factor of 10. The inset sketches the potential energy vs phase difference across the tunnel junction as well as the first three energy levels, $|0⟩$, $|1⟩$, and $|2⟩$. The resonance frequency ${\omega }_{10}/2\pi$ differs from ${\omega }_{21}/2\pi$ by a few percent.Reuse & Permissions

Figure 2

Circuit diagram and micrograph of the redesigned phase qubit. (a) A small-area ($A_J\sim 1\mu {\mathrm{m}}^2$) Josephson junction with little self-capacitance ($C_J=50\mathrm{fF}$) is shunted by a large ($A_C\sim 3600\mu {\mathrm{m}}^2$) high quality capacitor with $C_C=800\mathrm{fF}$. The qubit bias current $I_J$ is induced through an inductor with $L=720p\mathrm{H}$. (b) A scanning electron microscope image of the small-area Josephson junction shows well-defined features at submicron length scales. (c) An optical image of the shunting capacitor and the Josephson junction (white circle).Reuse & Permissions

Figure 3

Experimental results using the capacitively shunted phase qubit design. The vertical axis of each plot displays the probability $P_1$ of occupying the $|1⟩$ state. All results are obtained at a bias where ${\omega }_{10}/2\pi =5.838\mathrm{GHz}$. (a) Rabi oscillations have a visibility of about 85% and decay at a rate consistent with the measured qubit relaxation time of $T_1\approx 110\mathrm{ns}$ [shown in (c)]. (b) The Ramsey fringes (detuning of 196 MHz) decay nonexponentially and are consistent with spectroscopic linewidths. We extract a dephasing time of $T_2^{*}\approx 90\mathrm{ns}$. The two 90° rotations used in the experiment were 4 ns long. (c) The impact of low-frequency $1/f$ noise can be significantly reduced using a spin echo sequence. We extract an intrinsic dephasing time of $T_2\approx 160\mathrm{ns}$. The duration of the two 90° and the 180° rotations was 5 and 8 ns, respectively. Measurement of the energy decay ($T_1$) is also plotted. The pulse duration was 6 ns.Reuse & Permissions

Figure 4

Schematic diagram of the microwave pulser. The amplitudes of the two quadrature components $I$ and $Q$ are added to obtain microwaves with adjustable amplitude and phase, and are then amplified by 26 dB. A filtered digital pulse is then used in a second mixer to produce a Gaussian-shaped microwave pulse.Reuse & Permissions

Figure 5

Probability $P_1$ of occupying state $|1⟩$ vs ${\mathrm{DAC}}_I$ and ${\mathrm{DAC}}_Q$, which control the amplitude of the $\widehat{y}$ and $\widehat{x}$ tomography rotations, for the input states (a) $|0⟩$, (b) $|1⟩$, (c) $(|0⟩+|1⟩)/\sqrt{2}$, and (d) $(|0⟩+i|1⟩)/\sqrt{2}$. The tomography pulse was 16 ns long, and the state preparation pulses for the 90° and 180° rotations were 4 and 8 ns long, respectively. All experiments were performed on resonance with ${\omega }_{10}/2\pi =5.838\mathrm{GHz}$, using 200 statistics. All axes have the same relative scale. The dashed black circle indicates a total pulse amplitude corresponding to a $\pi$ pulse at different phases. The white dots label the zero amplitude points, and the three white crosses indicate the measurements necessary for a simplified state tomography technique (used for Fig. 6). The inset in each plot shows the predicted probability map.Reuse & Permissions

Figure 6

State tomography of the Bloch vector during a Ramsey-type experiment. (a) Sequence of operations of the experiment. A resonant microwave pulse $I_{\mu \mathrm{m}}$ at frequency ${\omega }_{10}/2\pi =5.838\mathrm{GHz}$ is first applied to give a 90° rotation about the $\widehat{x}$ axis. An adiabatic bias pulse $I_J$ with rise and fall times of abut 1 ns is then applied for a time ${\tau }_d$, during which the qubit is detuned by 37 MHz. The final 90° tomography pulse occurs 8 ns following the end of the bias pulse to ensure proper settling of the bias current, and it is 4 ns long, which is short compared with the relaxation times. Each data point was taken with 2000 statistics and is separated in time by 0.1 ns. (b) Plot of $P_1$ vs ${\tau }_d$ for the three tomography pulses ${90}_X$, ${90}_Y$, and $I$. (c) Projections of the reconstructed quantum state on the $xy$ and $xz$ planes of the Bloch sphere. (d) Theoretical prediction of the evolution of the Bloch vector including relaxation using $T_1=110\mathrm{ns}$ and $T_2^{*}=90\mathrm{ns}$.Reuse & Permissions