Fast, high-fidelity Transmon readout with intrinsic Purcell protection via nonperturbative cross-Kerr coupling

TL;DR

This work tackles the bottleneck of dispersive readout by introducing junction readout, a minimal circuit modification that creates a nonperturbative cross-Kerr interaction $χ$ between a transmon and its readout resonator. By placing a Josephson junction in parallel with the capacitive link, the scheme achieves intrinsic Purcell protection and suppresses measurement-induced transitions while inducing a resonator Kerr nonlinearity that enables bifurcation-based readout. The authors demonstrate high-fidelity measurements, achieving an assignment fidelity of $99.4\%$ in $68$ ns and a QND fidelity of $98.4\%$ without external Purcell filters or near-quantum-limited amplifiers, with a cross-Kerr strength around $2χ/2π \sim -14$ MHz. These results establish junction readout as a hardware-efficient, scalable alternative to dispersive readout, compatible with multiplexing and capable of fast, high-fidelity qubit measurement with reduced hardware overhead, thanks to intrinsic Purcell filtering and a large state-dependent resonator response.

Abstract

Dispersive readout of superconducting qubits relies on a transverse capacitive coupling that hybridizes the qubit with the readout resonator, subjecting the qubit to Purcell decay and measurement-induced state transitions (MIST). Despite the widespread use of Purcell filters to suppress qubit decay and near-quantum-limited amplifiers, dispersive readout often lags behind single- and two-qubit gates in both speed and fidelity. Here, we experimentally demonstrate junction readout, a simple readout architecture that realizes a strong qubit-resonator cross-Kerr interaction without relying on a transverse coupling. This interaction is achieved by coupling a transmon qubit to its readout resonator through both a capacitance and a Josephson junction. By varying the qubit frequency, we show that this hybrid coupling provides intrinsic Purcell protection and enhanced resilience to MIST, enabling readout at high photon numbers. While junction readout is compatible with conventional linear measurement, in this work we exploit the nonlinear coupling to intentionally engineer a large Kerr nonlinearity in the resonator, enabling bifurcation-based readout. Using this approach, we achieve a 99.4 % assignment fidelity with a 68 ns integration time and a 98.4 % QND fidelity without an external Purcell filter or a near-quantum-limited amplifier. These results establish the junction readout architecture with bifurcation-based readout as a scalable and practical alternative to dispersive readout, enabling fast, high-fidelity qubit measurement with reduced hardware overhead.

Figures (22)

• Figure 1: Circuit implementation of junction readout. (a) Schematic of a single qubit–resonator pair on the device. The circuit contains three flux loops: two large loops that enclose both the qubit and the resonator, highlighted by the red dashed and blue dash–dotted outlines, and a smaller loop formed by the asymmetric SQUID of the transmon, shown in green. (b) Optical micrograph of the first qubit-resonator pair. (c) Scanning electron microscope (SEM) image of the transmon qubit and its coupling to the resonator. (d) SEM images of the coupling junction (highlighted in blue) and the asymmetric SQUID of the transmon (highlighted in green).
• Figure 2: Circuit parameters. (a) Qubit frequency, (b) qubit anharmonicity and (c) cross-Kerr shift as a function of flux threading the transmon's asymmetric SQUID. The solid black lines are fits obtained from \ref{['Eq:Hamiltonian']} from which we extract $E_{J_c}/2\pi = 4.01$ GHz, $J/2\pi = 83.0$ MHz, and resonator impedance $Z_r = 68.8 \: \Omega$. (d) Calculated contributions of the transverse and nonperturbative coupling terms. In all panels, the vertical dashed line marks the flux bias point used for the readout characterization in the following sections.
• Figure 3: Intrinsic Purcell protection and critical photon numbers. (a) Purcell-limited relaxation time $T_1^{\rm pl}$ (green circles) and relaxation time $T_1$ (orange circles) as a function of flux threading the transmon SQUID. The inset shows a zoom of the $T_1$ revealing two distinct peaks corresponding to the notch frequency encountered twice over one flux quantum. The solid black line shows the theoretical prediction obtained from master-equation simulations using the fitted parameters from \ref{['Fig:flux_response']}. The blue star marks the operating point used for power calibration, while the gray vertical dashed line indicates the flux bias at which Purcell filtering is maximal and which is used for the readout characterization in subsequent sections. (b) Absolute value of the exchange matrix element $\vert \bra{0,1}\hat{H}_{\mathrm{int}} \ket{1,0} \vert$, illustrating the suppression of the qubit–resonator exchange coupling due to cancellation between the the $\hat{n}_t \hat{n}_r$ and $\sin{\hat{\varphi}}_t \sin{\hat{\varphi}}_r$ interaction terms. The red vertical dashed–dotted line indicates the balanced-coupling condition. (c) Onset of measurement-induced state transitions $n_{\mathrm{crit}}$ as a function of external flux. Blue dotted vertical lines indicate multiphoton resonances, which give rise to sharp drops in $n_{\mathrm{crit}}$. The gray vertical dashed line again marks the flux point of maximal Purcell protection, while the red dashed–dotted lines denote the balanced-coupling point.
• Figure 4: Single-shot readout performance. (a) Pulse sequence used for readout fidelity characterization: a preselection pulse heralds the qubit to the ground state, after which the qubit is optionally excited and read out. (b) Time evolution of the intracavity photon number for the qubit in $\ket{g}$ (blue) and $\ket{e}$ (red). The dashed line marks the end of the readout pulse and integration window. (c) $5 \times 10^{4}$ single-shot readout events for when the qubit is prepared in the excited (red) and ground (blue) states. The dashed line indicates the linear discriminant used to calculate the assignment fidelity. (d) Histograms of the measured quadrature distributions in (c). The solid black lines show fits to a double Gaussian distribution. The blue and red shaded regions indicate readout errors arising from qubit decay or excitation during the measurement. Taking half of each shaded area gives their contribution to the total error ($\epsilon_e = 0.35$ % and $\epsilon_g = 0.07$ %). The overlap of the two distributions (half of the green shaded area), contributes a state-separation error of $\epsilon_{\rm sep} = 0.18$ %. The resulting assignment fidelity is $99.4$ % with an integration time of $68$ ns.
• Figure 5: Readout fidelity landscape. (a) Heat map of the readout fidelity as a function of drive frequency $\omega_d$ and readout drive amplitude. The star indicates the parameter used for Fig. \ref{['Fig:ReadFidelity']}. The dashed colored line indicate the resonator bistable region for when the qubit is in state $\ket{g}$ (blue) and $\ket{e}$ (red). The gray dashed lines correspond to the drive frequency and amplitude used in the subsequent panels. (b,c) Intracavity photon number as a function of drive frequency (b) and drive amplitude (c), extracted from the Stark-shift calibration. Solid lines show fits to the stable solution of Eq. \ref{['eq:nonlinear dynamics']}, while light dashed lines indicate the regions of unstable solutions. Vertical black dashed lines indicate (b) the drive frequency and (c) the drive amplitude at the star marked parameters in (a).