Decoherence of a tunable capacitively shunted flux qubit

Abstract

Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. We find that for high qubit frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. Our results characterize decoherence in a realistic setup for quantum annealing and are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence.

Figures (6)

• Figure 1: The capacatively shunted flux qubit device. (a) Schematic of the CSFQ, with the $X$-loop in red, $Z$-loop in green, readout circuit in blue and control circuit in purple. Readout is performed by measuring the transmission through an rf-SQUID coupled inductively to the qubit.(b) Optical images of the qubit and interposer chips, around the CSFQ. The qubit and readout-SQUID loops are highlighted in false color. The two chips are flip-chip bonded with Indium bumps.
• Figure 2: Characterization of the symmetry point as a function of flux bias. (a) Transmission measurement versus the qubit external flux biases $\Phi_z, \Phi_x$. The black markers correspond to extracted $\Phi_z^\text{sym}$ by finding the point of reflection symmetry for each $\Phi_x$ trace in the transmission measurement, and the blue line is a fit to the analytical expression. (b) $Z$-loop bias symmetry point $\Phi_z^\text{sym}$ as a function of $\Phi_x$, extracted from the measurement shown in panel (a) (black triangles), and calculated from the analytical (blue line) and numerical (orange dots) model respectively. The inset shows the difference between the analytical and numerical models, and the gray shaded region corresponds to the range of $\Phi_x$ in which coherence measurements are performed in this work. The difference in $Z$-loop symmetry point from the analytical and numerical models is always below $1.5$ m$\Phi_0$ in this range, and approaches zero as $\Phi_x$ is reduced towards zero.
• Figure 3: Simulated qubit persistent current and energy gap as a function of flux bias. Left axis, the simulated qubit persistent current $I_p$ versus $X$-loop external flux bias $\Phi_x$, obtained using the circuit operator (black) and fitting to two-state approximation (light blue dashed) (see subsection "Device characterization" for detail). Right axis, the simulated qubit tunneling amplitude $\Delta$ versus $X$-loop external flux bias $\Phi_x$.
• Figure 4: Relaxation time $T_{1}$ as a function of flux bias. (a) Measured (black square markers) and simulated $T_{1}$ values as a function of $\Phi_x$, at the $\Phi_z$ symmetry point. Each measured point is the result of averaging 30 repeated measurements, and error bars are the standard deviation. The simulated $T_1$ considered contributions from different sources, with the combined simulated $T_1$ shown in black. The grey dashed line shows (for reference only) the simulated $T_1$ decay rate if the intrinsic flux follows $1/f^{0.96}$ instead of $1/f$ spectrum. (b) Measured (black square markers) and simulated (lines) qubit frequency $\Delta$ as a function of $\Phi_x$, at the $\Phi_z$ symmetry point. (c) Measured (solid markers) and simulated (lines) $T_{1}$ as a function of $\Phi_z$ at $\Phi_x = 0.32~\Phi_0$ (green circles), $0.36~\Phi_0$ (blue squares), and $0.4~\Phi_0$ (orange triangles). The simulated $T_1$ combines all noise sources shown in panel (a). There are no free parameters in the simulation; the flux noise amplitudes are obtained by fitting to the dephasing measurements for a fixed value of $\alpha$. See "Dephasing times" subsection in the text.
• Figure 5: Dephasing time as a function of flux bias. (a) Measured (solid markers) and simulated (lines) relaxation time $T_1$ (black circles), Ramsey $T_\phi$ (blue triangles) and spin-echo $T_\phi^E$ (red squares) dephasing times, as a function of $\Phi_x$, with $\Phi_z$ set at the symmetry point. Each measured point is the result of averaging 30 repeated measurements, and error bars are the standard deviation. (b) Measured (solid markers) and simulated values (lines) of $T_\phi$ as a function of $\Phi_z$ at $\Phi_x = 0.32~\Phi_0$ (green circles), $0.36~\Phi_0$ (blue squares), and $0.4~\Phi_0$ (orange triangles). The vertical dashed lines indicate the position of the $Z$-loop symmetry point at each value of $\Phi_x$.