Rapid High-fidelity Multiplexed Readout of Superconducting Qubits

The duration and fidelity of qubit readout are critical factors for applications in quantum-information processing as they limit the fidelity of algorithms which reuse qubits after measurement or apply feedback based on the measurement result. Here we present fast multiplexed readout of five qubits using a single 1.2-GHz-wide readout channel. Using a readout pulse length of 80 ns and populating readout resonators for less than 250 ns, we find an average probability of correct assignment for the five measured qubits to be $97\mathrm{\%}$. The differences between the individual readout errors and those found when measuring the qubits simultaneously are within $1\mathrm{\%}$. We employ individual Purcell filters for each readout resonator to suppress off-resonant driving, which we characterize by measuring the dephasing imposed on unintentionally measured qubits. We expect the readout scheme presented here to become particularly useful for the selective readout of individual qubits in multiqubit quantum processors.

Figure 1

(a) Schematic of the multiplexed readout experiment showing a circuit diagram of the superconducting chip at $T\approx 20$ mK and the room-temperature (RT) electronics. Multifrequency pulses used for readout are synthesized with a digital signal processing (DSP) unit, then up-converted to microwave frequencies by analog mixing with a local oscillator (LO) field, and applied to the input port of the feedline after several stages of attenuation. The readout signal emitted from the sample is amplified, down-converted, and digitized with an analog-to-digital converter (ADC) and further processed with the same DSP unit used for pulse synthesis. (b) Qubit lifetime $T_1$ limited by the Purcell effect vs detuning between the readout qubit and readout resonator ${\mathrm{\Delta }}_q$ with (blue solid line) and without (red dashed line) Purcell filter. The dashed gray horizontal line at $T_1=5\mu \mathrm{s}$ indicates typical $T_1$ times measured in this work. (c) Calculated photon number in the readout resonator with ${\kappa }_{\mathrm{R}}/2\pi =20\mathrm{MHz}$ normalized to its maximum value as a function of drive detuning $\mathrm{\Delta }={\omega }_d-{\omega }_{\mathrm{R}}$ with (blue solid line) and without (red dashed line) Purcell filter.

Figure 2

(a) False-colored optical micrograph of the device with qubits $\mathrm{Q}i$ (red), readout resonators $\mathrm{R}i$ (blue), Purcell filters (green), coupling resonators (orange), charge lines for single-qubit manipulation (purple), flux lines for single-qubit tuning (dark blue), and a common feedline (yellow). The ports used for probing the device are denoted in circles. (b) Enlarged view of $\mathrm{Q}3$ with its readout resonator and Purcell filter. (c) Cross-shaped single-island flux-tunable transmon qubit inductively coupled to a flux line, capacitively coupled to a readout resonator, two coupling resonators, and a charge line. (d) Interdigitated capacitor between the Purcell filter and the feedline.

Figure 3

(a) Transmission spectra $|S_{\mathrm{out},i}({\nu }_d)|$ of the readout resonators normalized to their respective maximum values measured from the charge line ports $i$ to the feedline output port as a function of drive frequency ${\nu }_d$ with resonance frequencies (dashed vertical lines) obtained from Lorentzian fits. (b) Transmission spectrum $|S_{\mathrm{out},\mathrm{in}}({\nu }_d)|$ measured from the feedline input to the output port close to the resonance frequency of $\mathrm{R}6$ with (red line) and without (blue line) a $\pi$ pulse applied to qubit $\mathrm{Q}6$ prior to measurement. The dashed lines are fits to the model described in Appendix pp3 with vertical dashed lines indicating the fitted readout resonator frequencies for the two cases.

Figure 4

Measured quadrature amplitude $A$ as a function of time $t$ when applying a square pulse (light blue) of length ${\tau }_p=80\mathrm{ns}$ resonant with $\mathrm{R}6$ and for the qubit $\mathrm{Q}6$ prepared in the excited (red) and ground (blue) state and the difference of the two (gray).

Figure 5

Histograms of integrated single-shot readout signal of $\mathrm{Q}2$ and $\mathrm{Q}6$, respectively, prepared with a $\pi$ pulse (red) and without (blue). The signal $s$ is normalized by the width of the Gaussian distribution. Experimental data (points) are shown with fits to a double Gaussian distribution (solid lines). Results from the individual readout experiment ($\bullet$) are compared to the case in which the readout pulse is also applied to all other qubits initially prepared in either a ground state (darker shade, $\times$) or averaged over all possible input states (brighter shade, $\circ$).

Figure 6

Assignment probability matrix $P(s|\zeta )$ for each qubit $\mathrm{Q}i$ prepared with a $\pi$ pulse ${\zeta }_i=\pi$ (red) or without a pulse ${\zeta }_i=0$ (blue) and each qubit assigned to either ground state $s_i=g$ (blue) or excited state $s_i=e$ (red). The qubits are ordered as $\mathrm{Q}2$, $\mathrm{Q}3$, $\mathrm{Q}5$, $\mathrm{Q}6$, and $\mathrm{Q}7$ from left to right (top to bottom) for the prepared (assigned) state.

Figure 7

(a) Contrast of the Ramsey oscillations $c$ of qubit $\mathrm{Q}7$ as for different readout pulse amplitudes $\xi$ relative to the final readout amplitude on $\mathrm{Q}3$ (dots) and a Gaussian fit (red line). (Inset) Pulse scheme used for the dephasing measurement consisting of 10-ns $\pi /2$ pulses (pink) and 80-ns readout pulses (yellow). (b) The average dephasing rate of qubit $\mathrm{Q}i$ when applying a readout pulse to qubit $\mathrm{Q}j$. Experimentally measured rates (filled bars), calculated values based on the parameters extracted from the spectroscopy shown in Table 1 (black frames), and calculated dephasing rates for a Gaussian-filtered probe pulse (red frames).

Figure 8

Detailed schematic of the measurement setup. The colored background on the left side indicates the different temperature stages for the components. In the panels on the right we describe in more detail down-conversion (DC), up-conversion (UP), warm amplification (WAMP) boards, components used around traveling waveguide parametric amplifier (TWPA) and virtual hardware components of the Zurich Instruments UHFLI-QC. UHFLI-QC includes an internal arbitrary waveform generator (AWG), logging units (log), timetrace averager (AVG), and complex weighted integration units. The amplification chain includes a high-electron-mobility transitor (HEMT), intermediate-frequency (IF), low-noise (LN), and ultralow-noise (ULN) amplifiers.

Figure 9

Input-output network of the readout circuit including feedline, Purcell filter, and readout resonator with input and output ports (green circles), resonator modes (yellow circles), traveling mode amplitudes (arrows), dissipation channels (wiggly arrows), and capacitive couplings of the elements.

Figure 10

Mode function and circuit model for the $\lambda /4$ resonator with capacitances $C_0$ and $C_c$ to ground at distances $d$ and $x_c$ from the terminated end, respectively.

Figure 11

Correlation coefficients between the outcomes of the multiplexed single-shot measurements as calculated by Eq. (E1).

Figure 12

Cross fidelity calculated using Eq. (E2). The diagonal elements correspond to the single-qubit readout fidelities.