A scalable edge-pass Purcell filter for high-fidelity readout of superconducting qubits

AI summary

Overview

Research area: Superconducting quantum computing hardware — specifically readout engineering and qubit-coherence protection for scalable processors.

Technical level: Intermediate. The paper assumes familiarity with dispersive readout, Purcell decay, and microwave filter design, but the core argument is accessible to anyone who knows the basics of circuit QED.

Scope (one sentence): The paper introduces, fabricates, and benchmarks "edge-pass" Purcell filters — high-pass and low-pass lumped-element networks that separate the readout band from the qubit band with a single transmission edge — and demonstrates high-fidelity readout, single-qubit gates, enhanced qubit lifetimes, and a built-in reset channel on planar and flip-chip devices.

What This Paper Is About

In a superconducting processor, qubits are read out by coupling them strongly to a readout resonator connected to a transmission line. That same strong coupling lets the qubit leak its excitation into the line and decay (the Purcell effect), so faster readout tends to shorten qubit lifetime. Conventional Purcell filters solve this with band-pass structures, but their finite passband and large coplanar-waveguide footprint make it hard to fit many readout resonators into the band as qubit counts grow. The authors replace the bounded passband with a single sharp transmission edge, so readout resonators can be placed freely on the transmitting side while the qubit sits in the stopband.

Key Contributions

1. A new filter topology concept ("edge-pass"). Rather than confining readout to a finite passband, the design separates the readout band and the protected qubit band by one cutoff frequency. Depending on whether the transmitting band is above or below the cutoff, the same building block yields a high-pass filter (HPF) or a low-pass filter (LPF), so one design procedure covers both.

2. A compact, scalable two-section lumped-element implementation. Each device is a two-section network in which identical one-section Chebyshev type-I units terminate the input and output ports, bridged by a coupling feedline. Because response is set by lumped L and C values rather than by wavelength-scale resonators, the filter is substantially more compact than a CPW-resonator filter of comparable performance. Filters of order 5, 7, 9, 11, and 13 were fabricated on a planar HPF chip (P-HPF) and on flip-chip HPF (F-HPF) and LPF (F-LPF) chips.

3. Experimental demonstration of high-fidelity readout and gates inside the filters. The HPF reached an average readout fidelity of 99.46(4)% (best qubit 99.56%) with a 150-ns pulse; the LPF reached 99.49(3)% (best 99.57%) with a 130-ns pulse. Average single-qubit gate fidelities from randomized benchmarking were 99.94% (HPF) and 99.93% (LPF) over three qubits per device.

4. Quantified Purcell protection plus a dual-use intrinsic "dissipation mode." Measured relaxation times exceed the filter-free Purcell limit and improve with filter order, and the standing-wave mode created by terminating the feedline with two filter sections is used as a reset channel, unifying readout, protection, and reset in one element.

Main Findings

• Readout is not degraded by the filter. Because readout resonators sit in the transmitting band, the readout signal passes with little attenuation. Single-shot IQ scatter plots show well-separated state distributions in both HPF and LPF devices, with fidelities obtained from projection histograms.

• Gate fidelities remain high. Randomized benchmarking of three qubits per device gave 99.94% (F-HPF) and 99.93% (F-LPF), indicating the filters are compatible with high-performance single-qubit control.

• Lifetime increases monotonically with filter order. On the P-HPF chip, which hosts 5th- to 11th-order filters with identical qubit and resonator distributions (so order is the only variable), measured average qubit lifetimes rose systematically with order.

• Measured lifetimes beat the filter-free Purcell limit. Using the reference T₁^no filter = Δ_qr² / (κ_r g_qr²), with resonator linewidths κ_r/2π = 6.85, 5.58, and 2.58 MHz for qubits H₁–H₃ and 10.00, 12.61, and 3.00 MHz for L₁–L₃, the measured relaxation times for the 11th-order HPF and LPF clearly exceed the unfiltered limit.

• Simulations reproduce the trend. Black-box quantization, with the network represented by its admittance Y_q(ω) at the qubit port via T₁^Purcell = C_q / Re[Y_q(ω_q)], predicts the measured order dependence. Simulated spectra used cutoff ≈6.3 GHz (HPF) and ≈5.0 GHz (LPF), with resonators at 6.8 GHz and 4.6 GHz and external quality factor Q_c ~ 500.

• Two T₁ dips identify two dissipative modes. Simulated T₁ limits show a dip at the readout resonator (6.8 GHz for HPF, 4.6 GHz for LPF) and another at the dissipation mode (~5.7 GHz). Away from these modes the simulated T₁ flattens at a floor set by substrate loss assumed in the model, not by the Purcell effect.

• Reset via both modes, with very different speeds. In the 11th-order LPF, tuning the qubit into resonance with the resonator mode gave reset in a swap time of about 150 ns, while the dissipation mode required about 8.5 μs, reflecting the modes' differing linewidths. The dissipation-mode linewidth is set by filter order and can in principle be broadened to accelerate reset.

• The dissipation mode can be placed by geometry. Supplementary simulations on 13th-order devices show the dissipation-mode frequency scales roughly inversely with feedline length while the cutoff is nearly unaffected; practical lengths are 4–6 mm (HPF) and 5–10 mm (LPF), with higher harmonics approaching the qubit band beyond about 10 mm. A qubit at the center of a 5 mm feedline sits at a voltage node and decouples from the mode entirely.

• Two sections beat one. Supplementary comparison of 13th-order one- versus two-section filters shows the two-section design reaches a much higher T₁ limit at the qubit frequency, because a one-section filter leaves one side of the resonator unprotected.

• Asymmetric designs add layout freedom. With an m-order section at the input and an n-order section at the output, the dissipation-mode frequency stays nearly fixed while larger total order m+n steepens the roll-off and deepens the stopband. As an example, the HPF entry with m = 5, n = 5 at location 0.1 mm reads 3.61 × 10² μs at a qubit frequency of 5 GHz; LPF maps used 6.5 GHz. Values were generally higher at location 2.5 mm than at 0.1 mm.

Methodology in Plain English

The authors start from classical microwave filter synthesis. They pick a Chebyshev type-I low-pass prototype with 0.5-dB passband ripple, which gives a sharp roll-off at cutoff and a stopband whose rejection deepens monotonically with filter order. Scaling that dimensionless prototype to a chosen cutoff frequency and port impedance converts tabulated coefficients (g_k, listed for orders 5, 7, 9, 11, 13) into physical capacitances and inductances. The same equations produce the HPF and LPF, just with the transmitting band placed above or below the cutoff.

Physically, the elements are interdigital capacitors and spiral inductors, which keeps the footprint small and the layout regular. The HPF uses a cutoff near 6.5 GHz with readout resonators at 6.7–6.9 GHz and maximum qubit frequency near 4.9 GHz. The LPF uses a 5 GHz cutoff with resonators at 4.5–4.7 GHz and maximum qubit frequency near 6.3 GHz; because it needs larger element values, each capacitor is a pair of parallel interdigital capacitors and each inductor a double spiral, avoiding excessive airbridges and reducing insertion loss. Both use a coupling feedline of about 5 mm, long enough to host several resonators while keeping the dissipation mode far from the qubit.

Devices are made from 200-nm α-tantalum film on sapphire, patterned by photolithography and etching, with Manhattan-style Josephson junctions from double-angle evaporation and airbridges by lift-off. In flip-chip versions, qubits sit on a top chip and resonators, control lines, and filters on a carrier chip, joined by 9-μm indium bumps.

Measurements use standard dispersive readout with a Josephson parametric amplifier at the base stage, plus multilevel readout protocols in which higher transmon levels are included in state classification to suppress measurement-induced leakage assignment error. Readout fidelity is defined as F = ½[P(0|g) + P(1|e)]. Lifetimes are compared against the analytic filter-free Purcell limit and against black-box-quantization simulations. Transmission spectra are computed by finite-element simulation and then measured, and the two agree well.

Why This Matters

Impact on research. Bandwidth scarcity is a real bottleneck in scaling superconducting processors: as qubit counts grow, readout resonators must be squeezed into a narrow passband, complicating frequency allocation and wiring. The edge-pass idea removes that constraint in principle, and the demonstration that a single compact element can simultaneously provide fast readout, Purcell protection, and a reset channel reframes filter design as a multi-function hardware primitive rather than a passive add-on. The measured readout fidelities above 99.4% average with 130–150 ns pulses and gate fidelities above 99.9% establish that the approach does not trade away performance.

Real-world applications (potential):

• Quantum error correction cycles in superconducting processors, which require repeated, fast, high-fidelity measurement and reset of every qubit.
• Dense multi-qubit readout multiplexing, where many resonators must share a readout line without a tight bandwidth budget.
• Cryogenic wiring reduction in large dilution-refrigerator systems, since integrating three functions into one element reduces per-qubit footprint and control-line overhead.
• Reset-and-reuse schemes in algorithms and benchmarking that need qubits returned to the ground state quickly between shots.

Industry relevance. The work is a collaboration between Nanjing University and Tencent Quantum Laboratory, and it is explicitly framed around the manufacturability concerns that matter to industrial quantum hardware teams: compact lumped elements instead of wavelength-scale resonators, regular layouts, and demonstrated compatibility with both planar and flip-chip integration schemes used in large-scale devices.

Future Directions

• Accelerating dissipation-mode reset. The ~8.5 μs swap time is far slower than the ~150 ns resonator-mode reset. Because the mode's linewidth is set by filter order and can be broadened by decreasing it, faster dissipation-mode reset is predicted but not yet demonstrated.
• Experimental validation of the fully integrated architecture. The proposed scheme — coupling a qubit to the filter's dissipation mode either directly with strength g_qf or through a tunable coupler with strength g_cf — is presented as a design, and the authors state that experimental validation remains to be done.
• Extension to a full multi-qubit module. The current devices characterize individual qubits and small groups; demonstrating the architecture at module scale is named as necessary future work.
• Exploiting asymmetric configurations. Filters with different-order sections at the two ports add a layout degree of freedom; the paper supplies simulated T₁ maps for m, n = 5 to 13 but does not experimentally test asymmetric devices.

Target Audience

This paper is most useful to superconducting-qubit hardware engineers and device physicists working on readout chains, multiplexing, and cryogenic packaging; to quantum-architecture researchers planning wiring and frequency-allocation strategies for large processors; and to graduate students and postdocs in circuit QED who want a concrete, experimentally validated example of co-designing a passive microwave network to serve readout, coherence protection, and reset at once. Readers without a background in microwave filter synthesis will still follow the motivation and results, but the design section assumes comfort with scattering parameters, Chebyshev prototypes, and dispersive readout.

Authors’ abstract

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.