An experiment with a superconducting transmon reported much longer measured relaxation times in a gain-engineered |g⟩–|f⟩ encoding than in an undriven conventional |g⟩–|e⟩ encoding. At the highlighted operating point, where the gain interaction rate was 133 kHz, measured T1f was 2.22 ± 0.06 milliseconds and T1g was 1.67 ± 0.34 milliseconds. Relative to the undriven encoding, the reported decay-time ratios were 16.7-fold for T1f, 12.6-fold for T1g and 14.7-fold on average. At that setting, randomized benchmarking measured a single-qubit gate fidelity of 99.58 ± 0.01%, and fidelity remained above 99.55% across the explored gain range.
The comparison revealed a coherence cost
The comparison also showed a sharp coherence trade-off. Ramsey coherence—the extent to which an encoded state retains its quantum phase—was 7.49 ± 0.47 microseconds for the |g⟩–|f⟩ encoding, compared with 107.2 ± 2.8 microseconds for |g⟩–|e⟩. Echo coherence was 65 ± 4 microseconds versus 138 ± 6 microseconds, respectively. The reported ratios were a 14-fold reduction in Ramsey coherence and a 2.1-fold reduction in echo coherence.
A standard transmon, a selective pump
The device was a standard superconducting transmon coupled to a microwave cavity. The cavity served as both the readout resonator and a lossy buffer mode. The study’s question was whether this simple platform could carry an engineered noise bias while still supporting fast, high-fidelity operations.
The engineered process used a single-photon parametric pump on the transmon’s |e⟩–|f⟩ transition to create frequency-selective gain. Cavity loss made the exchange effectively unidirectional. Researchers validated the calibrated gain by measuring time dynamics and comparing them with numerical simulations. Relaxation traces were fit with simple exponential curves, while Ramsey and echo measurements were used to assess coherence in the gain-engineered encoding.
The measured response followed the cavity’s frequency scale
When the pump frequency was varied, the measured T1f response followed a Lorentzian curve, a peaked response with a characteristic width. Its full width at half maximum—the width measured at half the peak height—was 858 ± 36 kHz, matching the independently measured cavity decay rate of 858 kHz.
Simulations identified thermal population as a dominant experimental limitation. With modeled thermal population set to zero, simulated T1f reached 15.4 milliseconds near a gain interaction rate of 290 kHz. In a resonant-only model, T1f saturated at about 42 milliseconds; when the cavity linewidth was doubled, the corresponding saturation value was about 82 milliseconds.
Error-correction results remain simulated
The proposed error-correction extension was examined in numerical syndrome-extraction simulations—repeated checks used to identify errors—rather than in a hardware demonstration. For binomial and four-legged cat codes, three repeated measurements with a majority vote reduced both modeled metrics below the result from a single measurement using an undriven ancilla, the auxiliary system used for the check. In a separate GKP model, the targeted-quadrature Holevo variance, a measure of spread, fell while backaction in the conjugate quadrature was suppressed.
The experimental and simulated results therefore have different status. The laboratory work measured physical-qubit relaxation, coherence and single-qubit gate fidelity, while the proposed error-correction benefits came from models rather than hardware measurements. The reported gate values were calibrated but not otherwise optimized, so the authors treated them as lower bounds for coherence-limited fidelities.
The preprint and its supporting material
The document identifies itself as arXiv:2608.26018v1 [quant-ph], dated 26 August 2026, and is classified as a preprint. Its accompanying Supplementary Information documents the experimental setup, system parameters, decoherence model and theoretical engineered-gain model. The authors say the data and code are available from the corresponding authors upon reasonable request, and the numerical simulations used the Python-based open-source software QuTiP. The work reports support from the Swiss National Science Foundation Grant No. 200021_1972551, the Swiss Nanoscience Institute Fellowship Grant No. P2101, and Switzerland’s State Secretariat for Education, Research and Innovation.
Paper data and sources
Original title: The Gain-Engineered Transmon
Authors: Ian Yang, Francesco Adinolfi, Alessandro Bruno et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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