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arXiv:1905.08403 · Applied Physics Letters

Mechanical Purcell filters for microwave quantum machines

Agnetta Y. Cleland, Marek Pechal, Pieter-Jan Stas, Christopher J. Sarabalis, E. Alex Wollack, Amir H. Safavi‐Naeini

Published Dec 23, 2019• 13 citations
arXivHTMLPDF

Abstract

In circuit quantum electrodynamics, measuring the state of a superconducting qubit introduces a loss channel, which can enhance spontaneous emission through the Purcell effect, thus decreasing the qubit lifetime. This decay can be mitigated by performing the measurement through a Purcell filter, which strongly suppresses signal propagation at the qubit transition frequency. If the filter is also well-matched at the readout cavity frequency, it will protect the qubit from decoherence channels without sacrificing measurement bandwidth. We propose and analyze design for a mechanical Purcell filter, which we also fabricate and characterize at room temperature. The filter is composed of an array of nanomechanical resonators in thin-film lithium niobate, connected in a ladder topology, with series and parallel resonances arranged to produce a bandpass response. Their modest footprint, steep band edges, and lack of cross talk make these filters an appealing alternative to analogous electromagnetic versions currently used in microwave quantum machines.

DOI
10.1063/1.5111151

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In circuit quantum electrodynamics, measuring the state of a superconducting qubit introduces a loss channel, which can enhance spontaneous emission through the Purcell effect, thus decreasing the qubit lifetime. This decay can be mitigated by performing the measurement through a Purcell filter, which strongly suppresses signal propagation at the qubit transition frequency. If the filter is also well-matched at the readout cavity frequency, it will protect the qubit from decoherence channels without sacrificing measurement bandwidth. We propose and analyze design for a mechanical Purcell filter, which we also fabricate and characterize at room temperature. The filter is composed of an array of nanomechanical resonators in thin-film lithium niobate, connected in a ladder topology, with series and parallel resonances arranged to produce a bandpass response. Their modest footprint, steep band edges, and lack of cross talk make these filters an appealing alternative to analogous electromagnetic versions currently used in microwave quantum machines.
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.
The measurement fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is also known as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency. We present semiclassical and quantum analyses for the bandpass Purcell filter realized by E. Jeffrey et al. [Phys. Rev. Lett. 112, 190504 (2014)]. For typical experimental parameters, the bandpass filter suppresses the qubit relaxation rate by up to two orders of magnitude while maintaining the same measurement rate. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.
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.
Engineering the admittance of external environments connected to superconducting qubits is essential, as increasing the measurement speed introduces spontaneous emission loss to superconducting qubits, known as Purcell loss. Here, we report a broadband Purcell filter within a small footprint, which effectively suppresses Purcell loss without losing the fast measurement speed. We characterize the filter's frequency response at 4.3 K and also estimate Purcell loss suppression by finite-element-method simulations of superconducting planar circuit layouts with the proposed filter design. The filter is fabricated with 200 nm-thick niobium films and shows the measured bandwidth over 790 MHz within 0.29 mm2 of compact size owing to densely packed spiral resonators. The estimated lifetime enhancement indicates the effective protection of the qubit from Purcell loss. The presented filter design is expected to be easily integrated on existing superconducting quantum circuits for fast and multiplexed readout without occupying large footprint.
High-fidelity readout with strong Purcell protection of qubit coherence is essential for scalable superconducting quantum processors, yet the finite passband and sizable footprint of conventional band-pass Purcell filters make them hard to scale. Here we introduce a scalable edge-pass Purcell filter that separates the readout band from the protected qubit band by a single transmission edge, freeing the readout resonators from bandwidth constraint. Depending on whether the transmitting band lies above or below the cutoff, the compact network is realized as a high-pass filter (HPF) or a low-pass filter (LPF). The HPF reaches an average readout fidelity of 99.46(4)% (up to 99.56%) with a 150-ns pulse, and the LPF reaches 99.49(3)% (up to 99.57%) with a 130-ns pulse. The average single-qubit gate fidelities are 99.94% (HPF) and 99.93% (LPF). Relative to the filter-free Purcell limit, the filters substantially extend the qubit lifetime, and the Purcell protection deepens at higher filter order. In addition, an intrinsic dissipation mode of the filter offers a qubit-reset channel. This leads to a compact architecture that unifies fast, high-fidelity readout, Purcell protection, and effective reset within a single filter for large-scale fault-tolerant quantum computation.
In superconducting qubits, suppression of spontaneous emission is essential to achieve fast dispersive measurement and reset without sacrificing qubit lifetime. We show that resonator-mediated decay of the qubit mode to the feedline can be suppressed using destructive interference, where the readout resonator is coupled to the feedline at two points. This ``interferometric Purcell filter'' does not require dedicated filter components or impedance mismatch in the feedline, making it suitable for applications such as all-pass readout. We design and fabricate a device with the proposed scheme and demonstrate suppression of resonator-mediated decay that exceeds 2 orders of magnitude over a bandwidth of 400MHz400\phantom{\rule{0.1em}{0ex}}\mathrm{M}\mathrm{Hz}400MHz for a resonator linewidth of 13.8 MHz.