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A high-efficiency elementary network of interchangeable superconducting qubit devices

Nature Electronics volume 8, pages 610–619 (2025)Cite this article

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Abstract

Modular architectures could be used to scale quantum devices to the point of fault tolerance and utility. Such modularity is of particular value with superconducting qubits, where monolithically manufactured devices are limited in both system size and quality. However, although prototypical quantum device networks have been fabricated, the development of quantum systems with both interchangeability and high-fidelity operations remains challenging. Here we report a modular architecture for scaling quantum processors with reconfigurable and expandable networks. We develop a high-efficiency interconnect based on a low-loss detachable cable connection between two superconducting qubit devices. We overcome residual loss through a fast pump scheme, enabling intermodule SWAP efficiencies at the 99% level in less than 100 ns. We use the scheme to generate high-fidelity entanglement and operate a distributed logical dual-rail qubit. With an error rate of around 1%, our interdevice operations are at the threshold for fault tolerance.

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Fig. 1: Experiment overview.
Fig. 2: Fast sidebands between qubit and high-Q detachable bus.
Fig. 3: Intermodule swaps.
Fig. 4: Dual-rail operations in the detuned Raman regime.

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Data availability

The experimental data that support the findings of this study are available at https://doi.org/10.13012/B2IDB-6176441_V1 (ref. 70).

Code availability

The code used for the data analysis and visualization is available at https://doi.org/10.13012/B2IDB-6176441_V1 (ref. 70).

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Acknowledgements

The research was carried out in part in the Materials Research Lab Central Facilities and the Holonyak Micro and Nanotechnology Lab at the University of Illinois. We thank K. Chow and R. Goncalves for help with the fabrication, and B. DeMarco and A. Kou for critical reading of the manuscript. We acknowledge funding from the NSF Quantum Leap Challenge Institute for Hybrid Quantum Architectures and Networks (award no. 2016136), from the IBM-Illinois Discovery Accelerator Institute and the Army Research Office (grant no. W911NF-23-1-0096). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US government.

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Author notes

  1. These authors contributed equally: Michael Mollenhauer, Abdullah Irfan, Xi Cao.

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Michael Mollenhauer, Abdullah Irfan, Xi Cao, Supriya Mandal & Wolfgang Pfaff

  2. Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Wolfgang Pfaff

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  1. Michael Mollenhauer
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Contributions

M.M. designed the device. M.M., A.I. and X.C. developed the theory models, conducted the experiment and analysed the data. S.M., M.M. and A.I. developed and tested the sideband pumping scheme. The paper was written by M.M., A.I., X.C. and W.P., with comments from all authors. W.P. supervised the work.

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Correspondence to Wolfgang Pfaff.

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Extended data

Extended Data Fig. 1 Experimental setup and wiring.

Most of the wiring follows standard best practices71. Noteworthy components: Low Pass (LP) filters: probe lines: 12 GHz (K&L 5L250-10200); pump lines: 1.8 GHz (Minicircuits VLF-1800+). Output line configuration: double-stage isolators (Low Noise Factory LNF-ISCIC4 12A), HEMT amplifier (Low Noise Factory LNF-LNC4 8C); room temperature low-noise amplifier (Low Noise Factory LNF-LNR4 14C). Room temperature electronics: signal modulation and demodulation: Quantum Machines OPX+ and Quantum Machines Octave; external RF generators: SignalCore SC5511A; pump signal amplifier: Mini-circuits ZHL-1-2W-S+.

Extended Data Fig. 2 Cable bus characterization.

a, Setup used to probe the modes of the coaxial cable in a reflection measurement. The inner conductor of the cable protrudes into a tunnel in the modules and capacitively couples to a pin connected to the SMA flange. b, CAD drawing of one of the cable modules. Top half has been made transparent to show the cable inner conductor (green) and coupling pin (gold) inside. c, Example reflection measurements of 3λ/2 modes of two cables (left: NbTi cable; right: Al cable) obtained with a vector network analyser; only phase response shown here. Fits (solid lines) to the data yield Qb = 3 × 104 (NbTi) and 5 × 105 (Al).

Extended Data Fig. 3 Sample holder design.

a, CAD drawings for a single transmon module, based on27. (Top) Full holder assembly, with cable clamp and cable bus included. Top half of the model made transparent to show the sample chip and exposed cable bus. (Middle) Side view of the holder. Copper clamps on each end hold the sample in place. Inside each clamp, a BeCu spring holds the chip in place with an estimated force of 250 grams. Aluminum cable clamp fastens around the cable and then mounts onto the side of the holder. (Bottom) Front view of the holder. Copper clamps made transparent to show the spacing between the cable inner conductor and sample. b, Exploded view of the actual device. c, Electric field simulation of the Al coaxial cable mode within one of the square modules shown in Extended Data Fig. 2a (left), and the sub-cut-off waveguide, with the sample and circuit elements modeled inside (right). Holders, cable clamp, and chip clamps have been outlined.

Extended Data Fig. 4 Bus-mediated qubit-qubit cross-Kerr.

Measurement of the direct dispersive interaction between the two qubits. We have measured Ramsey fringes on qubit 1, 4 μs after qubit 2 was prepared in either \(\left\vert {\rm{g}}\right\rangle\) or \(\left\vert {\rm{e}}\right\rangle\). Solid lines: sinusoidal fits.

Extended Data Fig. 5 Sideband spectroscopy and additional time-domain measurements.

a,d, Excited state population of qubits 1 (red) and 2 (blue) as a function of frequency and device input power of the microwave drives. Markers indicate where time-domain data was taken. Circles: Ω/2π ≈ 5 MHz (Fig. 2c,d). Triangles: Ω/2π ≈ 7 MHz (b,e). Squares: Ω/2π ≈ 10 MHz (c,f). Pentagon: Ω/2π ≈ 11 MHz (g). Qubit 1 displays additional transition(s) crossing the sideband resonance near the triangle marker, resulting in a broadened and asymmetric oscillation pattern (note the different scale on the detuning axis in b).

Extended Data Fig. 6 Time-dynamics of resonant Raman transitions.

a, Raman transitions between qubits 1 (red) and 2 (blue), immediately after tuning both sidebands individually to 5 MHz. The simulation (solid lines) matches the data (circles) with a 0.36 MHz detuning term on the bus (Eq. (6)). b,c, Simulation of the excited state population for qubits 1 (red) and 2 (blue) as a function of the drive detuning and time, assuming tuned up sidebands and no bus detuning. d,e, Data for the detuned swaps for the left and right qubit. In the simulation plots, ‘X’ marks a point of interest: in ref. 22 this point corresponds to an entangling gate. Here, we only predict a concurrence of 0.91 at this point, lower than what can be achieved using the stroboscopic approach shown in Fig. 3e of the main text.

Extended Data Fig. 7 Tuning up gates between qubits.

a, Example of a smooth pulse used to generate the swap gate. For this pulse shown, T = 160 ns, teff = 120 ns, and σ = 4 ns. Blacked dashed lines represent the effective gate time length. b, Excited state population for the right qubit as a function of consecutive gates for different effective gate times. Triangles, squares, and circles correspond to effective gate times of 139, 139.5, and 141.5 ns, respectively. Here, the 141.5 ns gate is best, as the exponential decay is indicative of least residual coherent error. c,d, excited state population for qubit 1 (red) and 2 (blue) as a function of the sideband gates applied where Ω/2π ≈ 5 MHz. Circles are data, squares are from simulation. Half-swap pulses are tuned between qubit 1 and bus, full-swap pulses between bus and qubit 2. The optimal effective sideband gate times for the left and right qubits are 52.6 ns and 101.8 ns, respectively.

Extended Data Fig. 8 Repeatability measurements.

Each iteration is a separate cycle of a bus re-mounted to a qubit package, cooled down and measured. Exception is iteration 8, where the device was not disassembled and reassembled from iteration 7, but only thermally cycled. Different markers represent different qubit samples and packages. Together, iterations 1 and 6 are the ones during which the main experiment data were collected. We have obtained ‘clean’ Sideband oscillations with Ω/2π ≈ 5 MHz in all iterations but iterations 7 and 8; there, we achieved only Ω/2π ≈ 4.5 MHz before observing high-power effects. a, Relaxation times (solid red), Ramsey (solid blue), and echo decay times (open blue). b, Qubit-bus dispersive shift χ (green) and bus lifetime (purple) across each iteration.

Extended Data Table 1 System parameters
Full size table

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Mollenhauer, M., Irfan, A., Cao, X. et al. A high-efficiency elementary network of interchangeable superconducting qubit devices. Nat Electron 8, 610–619 (2025). https://doi.org/10.1038/s41928-025-01404-3

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