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arXiv:2312.06405

Optimizing Resonator Frequency Stability in Flip-Chip Architectures: A Novel Experimental Design Approach

Yuan Li, Tianhui Wang, Jingjing Hu, Dengfeng Li, Shuoming An

Published Dec 11, 2023• 0 citations
arXivHTMLPDF

Abstract

In multi-qubit superconducting systems utilizing flip-chip technology, achieving high accuracy in resonator frequencies is of paramount importance, particularly when multiple resonators share a common Purcell filter with restricted bandwidth. Nevertheless, variations in inter-chip spacing can considerably influence these frequencies. To tackle this issue, we present and experimentally validate the effectiveness of a resonator design. In our design, we etch portions of the metal on the bottom chip that faces the resonator structure on the top chip. This enhanced design substantially improves frequency stability by a factor of over 3.5 compared to the non-optimized design, as evaluated by the root mean square error of a linear fitting of the observed frequency distribution, which is intended to be linear. This advancement is crucial for successful scale-up and achievement of high-fidelity quantum operations.

DOI
10.48550/arxiv.2312.06405

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In multi-qubit superconducting systems utilizing flip-chip technology, achieving high accuracy in resonator frequencies is of paramount importance, particularly when multiple resonators share a common Purcell filter with restricted bandwidth. Nevertheless, variations in inter-chip spacing can considerably influence these frequencies. To tackle this issue, we present and experimentally validate the effectiveness of a resonator design. In our design, we etch portions of the metal on the bottom chip that faces the resonator structure on the top chip. This enhanced design substantially improves frequency stability by a factor of over 3.5 compared to the non-optimized design, as evaluated by the root mean square error of a linear fitting of the observed frequency distribution, which is intended to be linear. This advancement is crucial for successful scale-up and achievement of high-fidelity quantum operations.
Abstract In multi-qubit superconducting systems utilizing flip-chip technology, achieving high accuracy in resonator frequencies is of paramount importance, particularly when multiple resonators share a common Purcell filter with restricted bandwidth. Nevertheless, variations in inter-chip spacing can considerably influence these frequencies. To tackle this issue, we present and experimentally validate the effectiveness of a resonator design. In our design, we etch portions of the metal on the bottom chip that faces the resonator structure on the top chip. This enhanced design substantially improves frequency stability by a factor of over 3.5 compared to the non-optimized design, as evaluated by the root mean square error of a linear fitting of the observed frequency distribution, which is intended to be linear. This advancement is crucial for successful scale-up and achievement of high-fidelity quantum operations.
In superconducting quantum processors, the predictability of device parameters is of increasing importance as many labs scale up their systems to larger sizes in a 3D-integrated architecture. In particular, the properties of superconducting resonators must be controlled well to ensure high-fidelity multiplexed readout of qubits. Here we present a method, based on conformal mapping techniques, to predict a resonator's parameters directly from its 2D cross-section, without computationally heavy and time-consuming 3D simulation. We demonstrate the method's validity by comparing the calculated resonator frequency and coupling quality factor with those obtained through 3D finite-element-method simulation and by measurement of 15 resonators in a flip-chip-integrated architecture. We achieve a discrepancy of less than 2% between designed and measured frequencies, for 6-GHz resonators. We also propose a design method that reduces the sensitivity of the resonant frequency to variations in the inter-chip spacing.
Fast and high-fidelity qubit readout requires strong coupling between the readout resonator and the feedline. However, such coupling unavoidably enhances qubit decay through the Purcell effect. We present a four-pole broadband Purcell filter implemented on a 3D flip-chip platform to overcome this trade-off. The filter provides a flat 1 GHz passband centered at 7.68 GHz and achieves more than 45 dB suppression at typical qubit frequencies. We demonstrate the filter's compatibility with multiplexed readout using a test chip that integrates six floating readout resonators strongly coupled within the passband. The chip is fabricated using a 150 nm Niobium (Nb) thin-film process and characterized at 20 mK in a cryogenic measurement setup. We also develop an analytical model that accurately captures the filter response and determines the resonance frequencies and external quality factors of the floating resonators directly from their physical geometry, enabling rapid circuit synthesis and design optimization. The proposed design is compact and fabrication-tolerant, making it a practical solution for large-scale superconducting quantum processors.
Efficient qubit reset and leakage reduction are essential for scalable superconducting quantum computing, particularly in the context of quantum error correction. However, such operations often require additional on-chip components. Here, we propose and experimentally demonstrate a hardware-efficient approach to qubit reset and readout using a multi-mode Purcell filter in a superconducting quantum circuit. We exploit the inherent multi-mode structure of a coplanar waveguide resonator, using its fundamental and second-order modes for qubit reset and readout, respectively, thereby avoiding additional components. Implemented in a flip-chip architecture, our device achieves unconditional reset with residual excitation below 1\% in 220 ns, and a leakage reduction unit that selectively resets the second excited state within 62 ns with a residual ∣f⟩|f\rangle∣f⟩ population of 6.1\%, accounting for the readout error. Despite the qubits being directly coupled to the filter in our configuration, the measured relaxation times are not degraded owing to intrinsic Purcell protection provided by an auxiliary mode. To our knowledge, this is the first experimental trial that exploits different-order modes of a microwave resonator for distinct qubit operations, representing a new direction toward scalable, hardware-efficient quantum processor design.
This study primarily investigates variations in the radio-frequency (RF) performance characteristics of components within flip-chip packaged superconducting qubit chips. By comparing changes in the lumped-element parameters of identical qubit chip physical structures across different packaging architectures, we analyze the evolving trends in the qubits' energy dissipation models and nonlinear parameters. Simulation and numerical computation results reveal that the metal layers proximal to the chip surface and the microbumps within the flip-chip architecture significantly impact structural parameters such as the resonant frequency and self-capacitance of resonant elements (including the qubits and readout cavities). This influence manifests as an increase in self-capacitance, consequently leading to an overall decrease in resonant frequency. Furthermore, structures such as the XY/Z control lines and the qubit-readout cavity coupling elements exhibit coupling strength of different change trends due to the altered electromagnetic field distribution within the packaging structure. Additionally, the direction of electromagnetic field leakage during coupling undergoes a change.
Purcell filters, which serve to suppress electromagnetic radiation and enhance the readout efficiency of qubit, are an indispensable component in superconducting quantum chips. With the increasing scale of quantum chips, the requirements for the performance and scalability of Purcell filters are becoming more stringent. In this report, a novel four-stage Purcell filter that enables fast measurement without exacerbating environmental damping of the qubits is presented. The design approach of the filter is derived from the serial and parallel configurations of λ/4 resonant cavities. The filter exhibits exceptional passband-to-stopband isolation, reaching up to 40 dB of isolation within the transition range of 400 MHz. Furthermore, the filter boasts a wide bandwidth for both the stopband and the passband, with the stopband ranging from 4 to 5.5 GHz and the passband extending from 5.8 to 6.5 GHz. In terms of spatial arrangement, each filter can be connected to over ten readout resonators for qubit readout. This innovative Purcell filter will significantly contribute to the development of high quality, scalable superconducting quantum chips.