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arXiv:2411.07153

Design of Qubit Readout Circuit for Purcell-Rate Suppression by Two-Path Interference

Ahmad Salmanogli, Hesam Zandi, Mohsen Akbari

Published Nov 11, 2024• 0 citations
arXivHTMLPDF

Abstract

The Purcell effect, a common issue in qubit-resonator systems leading to both fidelity and nonclassicality losses is studied while its suppression is achieved using a novel qubit readout circuit design. Our approach utilizes a unique coupling architecture in which, the qubit first interacts with a filter resonator before coupling to the readout resonator. This configuration enables precise control over the Purcell decay rate and ac Stark factor without impacting on measuring time. The mentioned factor is highly sensitive to the coupling strength between the readout resonator and the filter, meaning that the factor adjustment directly impacts the qubit state detection. A major advantage of this design is that tuning the resonator-filter coupling strength is relatively straightforward, offering flexibility in fine-tuning ac Stark factor. This work extensively analyzes the system using full quantum mechanical theory, deriving the total Hamiltonian and investigates mode dynamics via quantum Langevin equations. Key parameters influencing the nonclassicality of output signals are also explored through quantum correlation metrics, including symplectic eigenvalues, quantum discord, and classical discord. The main goal is to find any compromises exsting between the ac Stark factor increasing and the quantum correlation created in the readout circuit. By optimizing the critical factors, by which the ac Stark factor mainly affected, the proposed design not only improves the distinguishability of the qubit states but also ensures robust nonclassicality in the output signals. Results demonstrate the potential of the proposed system to bridge the gap between a high fidelity readout and quantum correlation preservation in scalable quantum architectures.

DOI
10.48550/arxiv.2411.07153

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The Purcell effect, a common issue in qubit-resonator systems leading to both fidelity and nonclassicality losses is studied while its suppression is achieved using a novel qubit readout circuit design. Our approach utilizes a unique coupling architecture in which, the qubit first interacts with a filter resonator before coupling to the readout resonator. This configuration enables precise control over the Purcell decay rate and ac Stark factor without impacting on measuring time. The mentioned factor is highly sensitive to the coupling strength between the readout resonator and the filter, meaning that the factor adjustment directly impacts the qubit state detection. A major advantage of this design is that tuning the resonator-filter coupling strength is relatively straightforward, offering flexibility in fine-tuning ac Stark factor. This work extensively analyzes the system using full quantum mechanical theory, deriving the total Hamiltonian and investigates mode dynamics via quantum Langevin equations. Key parameters influencing the nonclassicality of output signals are also explored through quantum correlation metrics, including symplectic eigenvalues, quantum discord, and classical discord. The main goal is to find any compromises exsting between the ac Stark factor increasing and the quantum correlation created in the readout circuit. By optimizing the critical factors, by which the ac Stark factor mainly affected, the proposed design not only improves the distinguishability of the qubit states but also ensures robust nonclassicality in the output signals. Results demonstrate the potential of the proposed system to bridge the gap between a high fidelity readout and quantum correlation preservation in scalable quantum architectures.
Rapid reset and readout of qubit states are essential for quantum error correction, yet accelerating these operations through stronger coupling to a dissipative environment inevitably increases qubit decay via the Purcell effect. Here we present a broadband Purcell filter that decouples the reset and readout paths, enabling both operations to be independently optimized without compromising qubit coherence. The filter employs two engineered notches - an intrinsic notch and a bandstop notch - to provide broadband Purcell protection, together with an additional reset stub that creates a reset mode below the protected band. To enable fast reset while suppressing filter-mediated interactions between qubits, we couple each qubit to a dedicated reset resonator. We experimentally demonstrate Purcell-limited relaxation times exceeding 1 ms across a 1.2 GHz bandwidth, simultaneously with 500 ns readout without a Josephson parametric amplifier and 100 ns reset with 99.6% efficiency. The reset resonator is designed with a deliberate kappa-chi mismatch, which suppresses photon-shot-noise-induced dephasing by a factor of 70 compared to the readout resonator. Our work provides a scalable hardware solution that resolves the traditional trade-off between fast qubit operations and qubit protection, advancing the prospects for fault-tolerant quantum computing.
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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.
In circuit quantum electrodynamics, qubits are typically measured using dispersively coupled readout resonators. Coupling between each readout resonator and its electrical environment, however, reduces the qubit lifetime via the Purcell effect. Inserting a Purcell filter counters this effect while maintaining high readout fidelity but reduces measurement bandwidth and, thus, limits multiplexing readout capacity. In this Letter, we develop and implement a multi-stage bandpass Purcell filter that yields better qubit protection while simultaneously increasing measurement bandwidth and multiplexed capacity. We report on the experimental performance of our transmission-line-based implementation of this approach, a flexible design that can easily be integrated with current scaled-up, long coherence time superconducting quantum processors.
We introduce and analyze a dispersive qubit readout scheme where two-mode squeezing is generated directly in the measurement cavities. The resulting suppression of noise enables fast, high-fidelity readout of naturally weakly coupled qubits, and the possibility to protect strongly coupled qubits from decoherence by weakening their coupling. Unlike other approaches exploiting squeezing, our setup avoids the difficult task of transporting and injecting with high fidelity an externally generated squeezed state. Our setup is also surprisingly robust against unwanted non-QND backaction effects, as interference naturally suppresses Purcell decay: the system acts as its own Purcell filter. Our setup is compatible with the experimental state-of-the-art in circuit QED systems, but the basic idea could also be realized in other systems.
In superconducting quantum devices, Purcell filters protect qubit information from decaying into external lines by reducing external coupling at qubit frequencies while maintaining it at readout frequencies. Here, we introduce and demonstrate a novel Purcell filter design that places the readout resonator frequencies in a "linewidth plateau" below the filter's first resonant mode. This approach, based on direct admittance engineering, can simultaneously achieve strong qubit protection and nearly constant external coupling across a wide readout bandwidth, addressing the traditional tradeoff between these properties. We first present a lumped-element analysis of our filters. We then experimentally demonstrate a compact on-chip linewidth-plateau filter, coupled to four resonators across its approximately 1 GHz readout band. We compare the measured linewidths to numerical predictions, and show how the filter protects a frequency-tunable transmon qubit from external decay. We envision that our flexible design paradigm will aid in efforts to create multiplexed readout architectures for superconducting quantum circuits, with well-controlled external couplings.