Millisecond Coherence in a Superconducting Qubit

Improving control over physical qubits is a crucial component of quantum computing research. Here we report a superconducting fluxonium qubit with uncorrected coherence time $T_2^{*}=1.48\pm 0.13\mathrm{ms}$, exceeding the state of the art for transmons by an order of magnitude. The average gate fidelity was benchmarked at 0.99991(1). Notably, even in the millisecond range, the coherence time is limited by material absorption and could be further improved with a more rigorous fabrication. Our demonstration may be useful for suppressing errors in the next generation quantum processors.

Figure 1

(a) Optical image of the measured device. The antenna electrodes are attached directly to the weak junction of fluxonium, contributing to the total shunting capacitance and coupling the qubit to a copper box readout resonator (not shown). (b) Close up of the fluxonium loop formed by the weak junction (top left corner) and a chain of stronger junctions. (c) Measured frequencies and calculated charge operator $\widehat{n}$ matrix elements for transitions between the lowest three energy levels at the half-integer flux bias. Note, the qubit transition $|0⟩-|1⟩$ is allowed, albeit suppressed in comparison to transition $|1⟩-|2⟩$, and transitions $|0⟩-|2⟩$ and $|1⟩-|3⟩$ are dipole forbidden.

Figure 2

(a) Ramsey coherence time $T_2^{*}$ and energy relaxation time $T_1$, measured simultaneously and repeatedly over a period of 12 h. Lower panel shows the Ramsey fringe frequency $\mathrm{\Delta }\nu$, the fluctuations of which are contained within 100 Hz. (b) Ramsey fringe data averaged over the entire 12-h period. The solid line is the fit to a decaying sinusoid with characteristic time ${\overline{T}}_2^{*}=1.16\pm 0.05\mathrm{ms}$. (c) Energy relaxation data averaged across the same 12-h period. The solid line is an exponential fit with a time constant ${\overline{T}}_1=1.20\pm 0.03\mathrm{ms}$.

Figure 3

(a) Results of randomized benchmarking (RB). The red curve (solid markers) is the reference RB sequence with an average Clifford gate error rate of $(1.7\pm 0.2)\times {10}^{-4}$, which converts to the average fidelity of the physical gates used to generate the Clifford group of 0.99991(1) (see text). The eight other curves are the interleaved RB sequences, where each color marks a given interleaved gate. The relative uncertainty on the gate errors given in the caption is about 10%. (b) Results of purity benchmarking. Solid markers indicate the purity of the quantum state versus number of Clifford gates. The decay rate coverts to the average error due to decoherence of $0.6\times {10}^{-4}$, establishing an upper bound on the achievable average gate fidelity of 0.99994.

Figure 4

(a) Energy relaxation time $T_1^{01}$ of transition $|0⟩-|1⟩$ versus external magnetic flux ${\mathrm{\Phi }}_{\mathrm{e}}$. Marker color indicates two separate scans taken 24 h apart. (b) Energy relaxation time $T_1^{02}$ of transition $|0⟩-|2⟩$ versus flux. Red and green dashed curves represent the dielectric loss model with an effective loss tangent $1.5\times {10}^{-6}$ and $4.5\times {10}^{-6}$, respectively. The magenta curve is the limit imposed by quasiparticle tunneling across the fluxonium’s weak junction, characterized by an effective quasiparticle density $x_{\mathrm{qp}}=5\times {10}^{-9}$ (see text). (c) Schematic of the driving (straight arrow) and relaxation (wavy arrows) processes involved in measuring the relaxation rate ${\mathrm{\Gamma }}_{02}\equiv 1/T_1^{02}$. Thermal occupation of state $|2⟩$ is neglected. Details of the experimental procedure are provided in Supplemental Material [18], note 7.