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arXiv:2604.11722

First-principles study of dispersive readout in circuit QED

Angela Riva, Prakritish Gogoi, Nicolas Gheeraert, Serge Florens, Alex W. Chin, Alain Sarlette, Alexandru Petrescu

quant-phcond-mat.mes-hallSubmitted Apr 13, 2026• Announced Apr 14, 2026• 0 citations
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Abstract

The speed and fidelity of dispersive readout of superconducting qubits should improve by increasing the amplitude of the measurement drive. Experiments show, however, that beyond some drive amplitude there is always a saturation or drop in fidelity, often associated with a decrease in qubit energy relaxation time $T_1$. A simple Lindblad master equation does not capture the latter effect. More involved approaches based on effective master equations rely on strong assumptions about the spectra of the system and the bath and only partially agree with observations. Here, we perform a first-principles simulation of the full unitary dynamics of dispersive readout by considering the circuit QED Hamiltonian coupled to a microscopic model for the measurement transmission line, allowing for its arbitrary spectrum, including filters. Our access to the dynamics of the bath degrees of freedom allows us to investigate the emission spectrum of the system as a function of drive power. We show how the dependence of qubit $T_1$ on readout drive amplitude is sensitive to the details of the bath spectrum. In particular, we find that $T_1$ drops with increasing drive amplitude when a Purcell notch filter is placed at the qubit frequency, and that the Lindblad master equation shows general qualitative defects compared to the first-principles model.

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The speed and fidelity of dispersive readout of superconducting qubits should improve by increasing the amplitude of the measurement drive. Experiments show, however, that beyond some drive amplitude there is always a saturation or drop in fidelity, often associated with a decrease in qubit energy relaxation time T1T_1T1​. A simple Lindblad master equation does not capture the latter effect. More involved approaches based on effective master equations rely on strong assumptions about the spectra of the system and the bath and only partially agree with observations. Here, we perform a first-principles simulation of the full unitary dynamics of dispersive readout by considering the circuit QED Hamiltonian coupled to a microscopic model for the measurement transmission line, allowing for its arbitrary spectrum, including filters. Our access to the dynamics of the bath degrees of freedom allows us to investigate the emission spectrum of the system as a function of drive power. We show how the dependence of qubit T1T_1T1​ on readout drive amplitude is sensitive to the details of the bath spectrum. In particular, we find that T1T_1T1​ drops with increasing drive amplitude when a Purcell notch filter is placed at the qubit frequency, and that the Lindblad master equation shows general qualitative defects compared to the first-principles model.
Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit and resonator are appreciably hybridized. In this work we revisit this setting using a microscopic Bloch-Redfield approach, where dissipation is constructed in the eigenbasis of the coupled qubit-resonator Hamiltonian with a complete, frequency dependent, open system description of the transmission line environment. Here, we show that the Lindblad and Bloch-Redfield decay rates can be quantitatively different in the absence of driving, while in the driven case we demonstrate that the time-independent Redfield dissipator and its time-dependent generalization can show qualitatively different behaviors as a function of driving strength. Finally, we investigate the effects of driving in structured spectral densities, recovering the suppression of measurement-induced relaxation in the presence of a so called Purcell filter.
Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number-nonconserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e., Kerr interactions) shows that number-nonconserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly nonlinear degrees of freedom.
The performance of a wide range of quantum computing algorithms and protocols depends critically on the fidelity and speed of the employed qubit readout. Examples include gate sequences benefiting from midcircuit real-time measurement-based feedback, such as qubit initialization, entanglement generation, teleportation, and, perhaps most importantly, quantum error correction. A prominent and widely used readout approach is based on the dispersive interaction of a superconducting qubit strongly coupled to a large-bandwidth readout resonator, frequently combined with a dedicated or shared Purcell filter protecting qubits from decay. By dynamically reducing the qubit-resonator detuning and thus increasing the dispersive shift, we demonstrate a beyond-state-of-the-art two-state-readout error of only 0.25% in 100-ns integration time. Maintaining low-readout-drive strength, we nearly quadruple the signal-to-noise ratio of the readout by doubling the readout-mode line width, which we quantify by considering the hybridization of the readout resonator and its dedicated Purcell filter. We find excellent agreement between our experimental data and our theoretical model. The presented results are expected to further boost the performance of new and existing algorithms and protocols critically depending on high-fidelity fast midcircuit measurements. Published by the American Physical Society 2024
High-fidelity qubit readout in circuit QED requires suppressing relaxation due to the Purcell effect, typically achieved through the use of Purcell filters. A key limitation of existing Purcell filter implementations is their large footprint. In this work, we propose a compact notch Purcell filter based on a Josephson junction (JJ) chain embedded in series with the readout resonator. We analytically derive the conditions for operation in the dispersive regime using a lumped-element model, and validate the concept through an example design that is analyzed through both lumped-element and full electromagnetic simulations. The results indicate that the proposed architecture achieves a Purcell decay time exceeding 1 ms, with a dispersive shift and resonator linewidth of approximately 10 MHz, enabling fast, high signal-tonoise ratio readout. As typical of notch filters, also this solution exhibits an inherent parameter sensitivity. SQUIDs can be used for post-fabrication frequency tuning, at the expense of an increase of the number of required control lines.
Superconducting transmon qubits form the backbone of today's leading quantum processors, where high field dispersive readout relies fundamentally on the shape and temporal structure of microwave control pulses. While transmon qubits offer improved robustness against charge noise, their performance is still strongly influenced by environmental coupling, particularly the Purcell effect and by the spectral characteristics of the readout pulses used for state preparation and logic operations. In this study, we present a rigorous comparative analysis of qubit coherence dynamics using measurement under four relevant configurations: a single-step rectangular pulse without Purcell decay, a single-step pulse subject to Purcell-induced relaxation, a two-step shaped pulse without Purcell effects, and a two-step shaped pulse incorporating Purcell decay. By solving the time-dependent Lindblad master equation for a three-level transmon system, we illustrate how readout pulse shaping and Purcell filtering independently and jointly influence qubit population dynamics, excited-state lifetime, and the final-state fidelity. The results demonstrate that two-step readout pulse shaping significantly improves coherence by suppressing overshoot and reducing higher-level population transfer, while the inclusion of Purcell mitigation further stabilizes the dynamics and enhances fidelity. The most notable observation is that the combined application of pulse shaping and Purcell filtering produces the most stable and highest fidelity qubit state discrimination. This unified perspective constitutes the central novelty of our work. Such a comparative framework, integrating pulse engineering with environmental decay modeling, has received limited explicit treatment in prior literature. The findings provide critical insights for optimizing both readout protocols and quantum hardware design in large scale superconducting quantum systems.
Measurement backaction degrades dispersive readout of superconducting qubits even at modest drive strengths, often via the reduction of qubit lifetimes during readout. In this work, we theoretically and experimentally study this degradation and show how it can result from the interplay between detuned two-level systems (TLSs) and a drive-renormalized qubit spectrum. For modest to strong readout, the qubit emission spectrum becomes non-Lorentzian and depends sensitively on the readout drive frequency (even when measurement rate is fixed). We combine the readout-modified qubit emission spectrum with time-dependent perturbation theory to predict qubit lifetimes in the presence of a TLS bath. Master equation simulations and experimental measurements on a frequency-tunable transmon confirm these predictions quantitatively. In particular, we find that driving at the resonator frequency associated with the qubit ground state yields the narrowest qubit emission spectrum and the least lifetime degradation for a fixed measurement rate, providing a practical guideline for optimizing readout protocols in future quantum processors.