A Unified Open Quantum System Investigation of Leakage Suppressed Transmon Qubit Dynamics via Parametric Pulse Spectral Engineering, Purcell Limited Dissipation Control, and Dispersive Readout Phase Space Analysis
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.
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.
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.
To carry out quantum computations, it is necessary to construct a circuit containing several interconnected qubits and be able to readout its states with high fidelity. The transverse dispersive coupling between a qubit and a microwave cavity is the most common technique of qubit readout in cQED. However, despite important progresses, implementing a fast high fidelity readout remains a major challenge. Indeed, inferring the qubit state is limited by the trade-off between speed and accuracy due to Purcell effect and unwanted transitions induced by readout photons in the cavity.This work focuses on an experimental investigation of cross-Kerr coupling and its benefits for qubit state readout, providing high fidelity and maximizing QNDness. To build a new readout scheme based on direct cross-Kerr coupling we employed a qubit architecture called "transmon molecule".The direct cross-Kerr coupling is a key point to our readout scheme since it prevents the qubit from Purcell effect.In order to realise the full potential of this system, thorough measurements were taken of an existing system, and then an improved version was designed and fabricated using a new nano fabrication recipe.To improve the qubit and readout performance, we have optimized different parameters: the circuit geometry has been adjusted to reduce the amplitude of the microwave electrical field at the interfaces; the electric circuit parameters were optimized to reach large detuning between the readout and the transmon frequencies; unwanted dipolar coupling between the transmon qubit and the cavity was reduced to avoid the Purcell effect.The fabrication recipe was also investigated and improved to get rid of residuals of resist on the surface of the substrate so-called "Veil of Death", improve the quality of aluminum and reproducibility of Josephson junctions.The measurements demonstrating the quantum non-demolition readout with fidelity as high as 99.4% and relaxation time 5 times higher than before - 20 microseconds.
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
Abstract Superconducting quantum circuits are a leading platform for quantum-information processing, but their development requires expertise spanning device design, microfabrication, cryogenic operation, microwave control, and quantum characterization. In this work, we report the realization of a flux-tunable superconducting transmon platform and present an integrated workflow encompassing design, fabrication, measurement, and numerical modeling. The device consists of an Al/AlOx/Al transmon coupled to a three-dimensional microwave cavity operating in the circuit quantum electrodynamics (cQED) dispersive regime. Two-tone spectroscopy reveals a fundamental transition frequency of ω01=5.0122GHz and an anharmonicity of α/2π=−202.4MHz , corresponding to EJ/EC≈82.9 . Flux spectroscopy yields a cavity-qubit coupling strength of g/2π=260MHz , while the cavity linewidth gives a loaded quality factor of QL=6127 and a Purcell limit of T1Purcell≈82μs . Time-domain measurements yield coherence times of T1=17.4μs and T2∗=5.8μs . To investigate coherence and dissipation in the device, the experimental observations are analyzed within a Lindblad master-equation framework describing cavity photon loss and thermal excitation, qubit energy relaxation, and pure dephasing processes. Using a set of experimentally extracted parameters, the model reproduces the measured spectroscopic and time-domain observables, providing a quantitative description of the open-system dynamics of the transmon-cavity platform. The analysis shows that the measured coherence is primarily limited by pure dephasing and energy-relaxation processes, whereas thermal excitation plays a minor role under the experimental conditions. Inspired by the broader framework of quantum dissipation in macroscopic quantum systems pioneered by Caldeira and collaborators, this approach enables a quantitative analysis of relaxation and dephasing processes in superconducting quantum circuits. Beyond the characterization of a single device, the present work demonstrates the establishment of the expertise, infrastructure, and experimental workflow required for the design, fabrication, measurement, and modeling of superconducting quantum circuits, contributing to the development of quantum technologies in Brazil and related applications.
High-fidelity and rapid qubit readout is essential for superconducting quantum processors, typically realized through the quantum non-demolition (QND) dispersive interaction within a qubit-resonator architecture. However, the achievable readout speed and fidelity are fundamentally limited by measurement-induced state transitions (MIST). For a transmon qubit, MIST is highly sensitive to the offset charge ng due to the charge dispersion of its higher-lying energy levels. In this work, we systematically investigate ng-dependent MIST dynamics governed by the diabaticity and symmetry of pulse shaping within a charge-sensitive transmon architecture. We engineer fast-load and fast-clear pulses that effectively suppress resonator photon overshoots, thereby demonstrating a highly practical strategy to mitigate MIST without requiring complex waveforms or real-time feedback. Utilizing active gate-voltage control and rapid feedback, the measurement-induced transition probability is precisely mapped against ng and the steady-state resonator photon number, exhibiting strong agreement with numerical Floquet branch analysis. Ultimately, we evaluate the ng-averaged total error probabilities for both readout and post-readout stages, verifying that a straightforward three-step pulse scheme consistently minimizes overall readout errors. Within the framework of large-scale superconducting quantum processors, this practical, hardware-free approach inherently offers a better trade-off between the readout signal-to-noise ratio and QND preservation.
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 T1. 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 T1 on readout drive amplitude is sensitive to the details of the bath spectrum. In particular, we find that T1 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.