A quasiparticle-protected superconducting qubit

The gist: Engineering the quasiparticle energy landscape beyond Josephson junctions can substantially increase qubit resilience while identifying remaining limitations relevant to both radiation-induced error bursts and superconducting circuits operated near optical fields.

Motivation

Superconducting circuits are vulnerable to quasiparticles (QPs) generated by high-energy radiation or optical fields, which can induce relaxation by tunneling across a Josephson junction (JJ) The resulting correlated error bursts are not correctable with standard quantum error-correcting codes When superconducting circuits are intentionally operated near optical fields, stray infrared photons can generate QPs that break Cooper pairs and create QPs Suppressing QP poisoning is thus a key requirement for superconducting circuits that must operate in proximity to optical fields

Methodology

The researchers extended gap engineering beyond the JJ by engineering the quasiparticle energy landscape of the transmon to keep QPs away from the junction leads The device combines a Nb/Au ground plane and island with strongly gap-engineered Al JJs They compare this Nb device with an all-Al transmon designed to reproduce the strongly gap-engineered devices of Ref. [30] The Al junctions were engineered by setting film thicknesses to tthick = 100 nm for the thicker, low-gap lead and tthin = 18 nm for the thinner, high-gap lead The Nb transmon uses a 150 nm sputtered Nb ground plane and qubit island Niobium is attractive for radiation-resilient circuits because nonequilibrium QPs can relax on nanosecond timescales much faster than the millisecond-scale QP lifetimes reported in Al

Key Findings

The Nb transmon withstands more than an order of magnitude higher optical power before excess relaxation appears compared to an all-Al transmon with nominally identical junctions Over the same power range, the Nb transmon shows no resolvable quasiparticle-induced frequency shift, consistent with a low QP density near the JJs Dephasing and state-preparation-and-measurement (SPAM) infidelity nevertheless increase with optical power even while relaxation remains protected

Limitations and Further Investigation

The protection is not complete, however, as dephasing and SPAM infidelity increase with optical power even while the relaxation rate remains unchanged The qubit transition frequency is sensitive to the Josephson energy EJ = Φ0Ic/2π QPs in the JJ leads suppress the critical current and consequently induce a downward shift of the qubit frequency δωq = ωq(Po)−ωq(0) which provides a probe of the QP population near the junctions While previous measurements found no significant difference in robustness among strongly gap-engineered qubits operated at different frequencies within the same protected regime, this frequency difference may contribute to the quantitative comparison The results suggest that engineering the quasiparticle energy landscape beyond the junction can substantially increase qubit resilience while identifying remaining limitations relevant to both radiation-induced error bursts and superconducting circuits operated near optical fields Further improvements will require identifying these remaining mechanisms and controlling QP generation, transport, and trapping throughout the device

Device Parameters

Table I summarizes the device parameters for the two transmons without laser light, showing that the Nb transmon has a maximum frequency ωq/2π of 4.404 GHz compared to 5.389 GHz for the Al transmon The qubit lifetime T1 is reported as 40–50 µs for both devices Ramsey coherence time T∗2 is estimated at 20–30 µs for the Nb transmon and 5–6 µs for the Al transmon

Optical Response

The internal quality factor of resonators made from Al and Nb shows that the loss in the Al resonator increases monotonically with Po, consistent with increasing distributed microwave loss from optically generated QPs The onset of degradation in the Nb transmon at high optical power could be caused by QPs tunneling across the JJs despite the engineered gap difference, for example after QPs absorb high-frequency phonons generated by recombination in the Nb film Modeling suggests that a QP density 500 times greater than in bulk Al is required in the bandages to cause similar quality factors between the transmon and resonator at Po = 100 nW The simulation results show that the required sheet resistance Rs to reproduce the measured QP-limited internal quality factor at Po = 100 nW is approximately 0.7 µomega/□ The simulation also shows that the transmon’s quality factor is not limited by bandage resistance below Rs ∼ 10 µomega/□

Conclusion

The researchers demonstrate a transmon architecture that extends gap engineering beyond the JJ by engineering the landscape of the superconducting gap across the entire device This approach increases the optical power required to induce excess relaxation by more than an order of magnitude compared to an all-Al transmon with nominally identical junctions The protection is not complete, however, as dephasing and SPAM infidelity increase with optical power even while the relaxation rate remains unchanged Promising directions include reducing the role of Al in the most QP-sensitive regions and exploring alternative junction materials Device-level control of quasiparticles provides a route toward superconducting qubits that better withstand both radiation-induced error bursts and nearby optical fields

Acknowledgments

The authors thank Amr Osman, Claudia Castillo-Moreno, Kunal Helambe, and Simon Sundelin for advice that enabled the fabrication of the samples The devices were fabricated in the MyFab Nanofabrication Laboratory at Chalmers W.W. acknowledges support in part by the Knut och Alice Wallenberg Foundation through a Wallenberg Scholar grant R.V.L. acknowledges support from the Knut and Alice Wallenberg Foundation through the Wallenberg Centre for Quantum Technology through a WACQT Fellowship, from the European Research Council via Starting Grant 948265, and from the Swedish Foundation for Strategic Research via grant FFL21-0039 S.G. acknowledges financial support from the European Research Council (Grant No. 101041744 ESQuAT), and from the Knut and Alice Wallenberg Foundation through the Wallenberg Centre for Quantum Technology (WACQT)

Appendix Details

Appendix A details the device design and parameters, including film thicknesses tthick = 100 nm for the thicker, low-gap lead and tthin = 18 nm for the thinner, high-gap lead Appendix B describes the measurement setup involving a dilution refrigerator and optical power control via a variable optical attenuator (VOA) Appendix C presents calculations of QP density in the Al resonator using Mattis-Bardeen theory Appendix D models the transmon with low-gap Al bandages and derives an estimate for the QP density in the bandages required to reproduce measured quality factors Appendix E performs eigenmode simulations to investigate the effects of QP poisoning of the bandages in the transmon Appendix F discusses hot quasiparticles and their coupling to a hot phonon bath, noting that this coupling may produce a QP energy distribution characterized by an effective temperature higher than that of the mixing chamber Appendix G describes transmon thermometry using Rabi oscillations to estimate the population in e⟩ after a passive reset Appendix H investigates how the relaxation rate of the Al transmon changes after laser pulses, showing a slow recovery consistent with slow QP relaxation and trapping in the JJs Appendix I discusses maximum optical power and compatibility with optically driven devices, noting that results are specific to the deliberately reflective package used

Table I Summary

The table summarizes the device parameters for the two transmons without laser light, showing that Nb has a maximum frequency ωq/2π of 4.404 GHz and T1 values of 40–50 µs The Al transmon has a maximum frequency ωq/2π of 5.389 GHz and T1 values of 40–50 µs The readout resonance frequencies are listed as ωr/2π = 6.705 GHz for Al and 6.624 GHz for Nb The thin-lead thickness tthin is 18 nm for both devices The thick-lead thickness tthick is 100 nm for the Al device and 18 nm for the Nb device The bandage thickness tbandage is 300 nm for both devices

Table II Summary

Table II presents estimated QP density in the Al resonator as a function of applied optical power and corresponding measured internal quality factor Q, showing that at zero optical power Q = 2.1 × 10 6 For Po ≥ 1 nW, excess energy loss relative to this value is assumed to be due to QPs The estimated QP densities increase with optical power, reaching a maximum of 5.

1. textbfQuasiparticle Poisoning Resilience in Qubit Design (Nb/Au Transmon): The improved system can withstand more than an order of magnitude higher near-infrared optical power before excess relaxation appears compared to all-aluminum devices, increasing the operational range for superconducting circuits near optical fields by a factor of ten.

2. textbfFrequency Stability Against Optical Fields: The system exhibits no resolvable quasiparticle-induced frequency shift over the same power range, suggesting that engineering the quasiparticle energy landscape can substantially increase qubit resilience to nearby optical fields, even while dephasing and SPAM infidelity increase.

3. textbfError Channel Identification: The improved system allows researchers to distinguish between relaxation protection and other errors, as dephasing and state-preparation-and-measurement (SPAM) infidelity increase with optical power even while relaxation remains unchanged, identifying additional error channels once QP-induced relaxation is suppressed.

4. textbfMaterial Engineering for Qubit Protection: The system demonstrates the benefit of engineering the quasiparticle energy landscape beyond the junction, suggesting future improvements should focus on reducing the role of Al in the most QP-sensitive regions and exploring materials like Niobium for enhanced radiation resilience.

5. textbfThermal Resilience Assessment: The system provides a method to assess qubit temperature under illumination, as it observe[s] no increase in the transmon’s excited-state population as we increase the optical power, confirming that residual excited-state population remains low even at higher optical powers.