Waveform-driven prediction of transmon qubit energy spectra using a physics-informed path-transformed transformer trained on Josephson junction dynamics.
Extracting the energy spectrum of a superconducting transmon qubit requires time-consuming microwave spectroscopy that must be repeated following every thermal cycle or parameter drift event. We introduce the Physics-Informed Path-Transformed (PaTH) Transformer, a surrogate model trained exclusively on resistively-shunted Josephson junction (RCSJ) numerical simulations, which predicts the five lowest energy eigenvalues and the anharmonicity from a raw DC voltage waveform. The model is trained on 10,000 simulated circuits spanning the realistic transmon parameter space (EJ /EC ∈ [10.7, 300], f01/h ∈ [2.6, 13.3] GHz) and evaluated on 1,500 independent test circuits, achieving mean absolute energy error 0.886 μeV (R2 ≥ 0.998 per level) and transition-frequency spacing error 2.14%, with GPU inference completing in 8.70 ms per circuit. A curriculum-ramped physics loss incorporating Josephson monotonicity, quantization spacing, anharmonicity sign, and Lindblad-Heisenberg constraints produces physically self-consistent predictions throughout training. Treating anharmonicity as a direct sixth output resolves a gradient-scale conflict (∼25× imbalance) that prevents reliable convergence when it is inferred post-hoc from level differences. The model delivers, from a single forward pass: DRAG gate fidelity ⟨F⟩ = 0.99982 at 3.9 ns; dispersive readout shift −14.3 MHz; macroscopic quantum tunneling crossover at 56.6 mK; SQUID tunable range 5.95 GHz; and inverse-design frequency errors below 0.05 kHz. Zero-noise extrapolation across five dilution-refrigerator temperatures confirms that model accuracy already reaches the Johnson-Nyquist noise floor, with the macroscopic quantum tunneling crossover temperature providing a physics-derived accuracy benchmark independent of model architecture. Validated against eight published experimental spectra from four independent laboratories, the surrogate achieves mean f01 error 1929 MHz versus 1935 MHz for exact Hamiltonian diagonalization, demonstrating that RCSJ waveform encoding conveys device-level physics that the static ideal Hamiltonian cannot represent.
Extracting the energy spectrum of a superconducting transmon qubit requires time-consuming microwave spectroscopy that must be repeated following every thermal cycle or parameter drift event. We introduce the Physics-Informed Path-Transformed (PaTH) Transformer, a surrogate model trained exclusively on resistively-shunted Josephson junction (RCSJ) numerical simulations, which predicts the five lowest energy eigenvalues and the anharmonicity from a raw DC voltage waveform. The model is trained on 10,000 simulated circuits spanning the realistic transmon parameter space (EJ /EC ∈ [10.7, 300], f01/h ∈ [2.6, 13.3] GHz) and evaluated on 1,500 independent test circuits, achieving mean absolute energy error 0.886 μeV (R2 ≥ 0.998 per level) and transition-frequency spacing error 2.14%, with GPU inference completing in 8.70 ms per circuit. A curriculum-ramped physics loss incorporating Josephson monotonicity, quantization spacing, anharmonicity sign, and Lindblad-Heisenberg constraints produces physically self-consistent predictions throughout training. Treating anharmonicity as a direct sixth output resolves a gradient-scale conflict (∼25× imbalance) that prevents reliable convergence when it is inferred post-hoc from level differences. The model delivers, from a single forward pass: DRAG gate fidelity ⟨F⟩ = 0.99982 at 3.9 ns; dispersive readout shift −14.3 MHz; macroscopic quantum tunneling crossover at 56.6 mK; SQUID tunable range 5.95 GHz; and inverse-design frequency errors below 0.05 kHz. Zero-noise extrapolation across five dilution-refrigerator temperatures confirms that model accuracy already reaches the Johnson-Nyquist noise floor, with the macroscopic quantum tunneling crossover temperature providing a physics-derived accuracy benchmark independent of model architecture. Validated against eight published experimental spectra from four independent laboratories, the surrogate achieves mean f01 error 1929 MHz versus 1935 MHz for exact Hamiltonian diagonalization, demonstrating that RCSJ waveform encoding conveys device-level physics that the static ideal Hamiltonian cannot represent.
Designing a superconducting qubit to realize specific Hamiltonian parameters typically requires iterating through a time and compute-intensive forward loop in which the designer chooses a layout geometry, simulates it, extracts circuit parameters such as capacitances, and refines the geometry. We study the inverse version of this task using a neural-network workflow that maps target Hamiltonian parameters directly to component-level layout parameters, which we subsequently demonstrate on a planar transmon layout. During training, we pair the inverse model with a frozen forward surrogate model and evaluate the loss in Hamiltonian space rather than in layout-parameter space. In validation against a conventional EM solver, 97% of generated designs produce usable geometries, and the inverse-plus-surrogate pipeline reaches mean percent errors of 0.73% for qubit frequency and 1.58% for anharmonicity, comparable to or below the fabrication and simulation-to-measurement uncertainty expected for academic-process transmon devices of this type. A single pipeline query takes ~60 ms on CPU, versus ~2 min for a conventional EM capacitance extraction on the same hardware, a speedup of approximately 2,000x. Batching minimizes the AI model inference overhead, reducing the runtime to 3.1 microseconds per sample on CPU and 2.6 microseconds per sample on GPU at a batch size of 2048, resulting in speedups of 3.9 x 10^7 and 4.6 x 10^7, respectively, relative to a single conventional CPU EM extraction. Our results indicate that component-level inverse design usefully extends and complements conventional EM simulation, including for small datasets on the order of 1,000 samples.
Abstract Superconducting quantum circuits are a leading platform for quantum-information processing, but their development requires expertise spanning device design, microfabrication, cryogenic operation, microwave control, and quantum characterization. In this work, we report the realization of a flux-tunable superconducting transmon platform and present an integrated workflow encompassing design, fabrication, measurement, and numerical modeling. The device consists of an Al/AlOx/Al transmon coupled to a three-dimensional microwave cavity operating in the circuit quantum electrodynamics (cQED) dispersive regime. Two-tone spectroscopy reveals a fundamental transition frequency of ω01=5.0122GHz and an anharmonicity of α/2π=−202.4MHz , corresponding to EJ/EC≈82.9 . Flux spectroscopy yields a cavity-qubit coupling strength of g/2π=260MHz , while the cavity linewidth gives a loaded quality factor of QL=6127 and a Purcell limit of T1Purcell≈82μs . Time-domain measurements yield coherence times of T1=17.4μs and T2∗=5.8μs . To investigate coherence and dissipation in the device, the experimental observations are analyzed within a Lindblad master-equation framework describing cavity photon loss and thermal excitation, qubit energy relaxation, and pure dephasing processes. Using a set of experimentally extracted parameters, the model reproduces the measured spectroscopic and time-domain observables, providing a quantitative description of the open-system dynamics of the transmon-cavity platform. The analysis shows that the measured coherence is primarily limited by pure dephasing and energy-relaxation processes, whereas thermal excitation plays a minor role under the experimental conditions. Inspired by the broader framework of quantum dissipation in macroscopic quantum systems pioneered by Caldeira and collaborators, this approach enables a quantitative analysis of relaxation and dephasing processes in superconducting quantum circuits. Beyond the characterization of a single device, the present work demonstrates the establishment of the expertise, infrastructure, and experimental workflow required for the design, fabrication, measurement, and modeling of superconducting quantum circuits, contributing to the development of quantum technologies in Brazil and related applications.
Abstract Fabrication-induced variation in Josephson junction parameters ---shunt capacitance~C, normal-state resistance~$\RN$, and superconducting gap~$\Dgap$---introduces uncertainty in transmon qubit frequencies and leads to residual ZZ crosstalk that limits multi-qubit gate fidelity. This work presents a quantitative, end-to-end simulation framework that maps junction-level disorder to GHZ state fidelity in a three-qubit fixed-coupling transmon array. Five concrete results are obtained. (1)~An analytic pipeline is constructed linking $(C,\RN,\Dgap)$ to qubit frequency ω01 and detuning Δ, enabling direct propagation of fabrication noise into gate-level error rates. (2)~Monte Carlo analysis with 2\% parameter variation shows that normal-state resistance dominates detuning uncertainty, producing σΔ=0.113\,GHz---approximately 1.4× larger than variations from C or $\Dgap$. (3)~Two error models are implemented and compared: a probabilistic depolarizing model and a coherent ZZ model using the anharmonicity-corrected dispersive shift ζZZ=g2(1/Δ−1/(Δ+α)). Because Model 1 encodes only the \emph{magnitude} of the coupling-induced error while Model 2 encodes its \emph{signed, oscillatory phase}, the two models are not interchangeable estimates of the same quantity: their predictions diverge by up to ∣ΔF∣≈0.66 in GHZ fidelity near the boundary of the perturbation-validity exclusion zone, with Model 2 alone capturing the periodic revivals in fidelity that a magnitude-only stochastic model cannot represent by construction. (4)~The coherent model identifies the breakdown of second-order perturbation theory at Δ≈∣α∣=0.248\,GHz, which, combined with fabrication-induced detuning spread, yields a conservative model-avoidance region Δ∈[0.02,0.47]\,GHz within which non-perturbative treatment is required for quantitative characterization. (5)~Model-selection guidance is established: the probabilistic model provides a conservative bound for threshold estimation, while the coherent model is required for accurate hardware characterization and mitigation design. Finally, the framework is structured to allow systematic extension to more realistic noise channels, including leakage, correlated fabrication disorder, and non-perturbative multilevel dynamics, providing a pathway toward experimentally validated device-level error modeling.
Abstract Quantum bits, or qubits, are an example of coherent circuits envisioned for next-generation computers and detectors. A robust superconducting qubit with a coherent lifetime of O(100 µs) is the transmon: a Josephson junction functioning as a non-linear inductor shunted with a capacitor to form an anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap between neighboring circuits. Simply transplanting our recipe optimized for single, stand-alone devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer) initially resulted in global drifts in room-temperature tunneling resistance of ± 30%. Inferring a critical current I c variation from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in < 3.5% relative standard deviation (RSD) in critical current ( ≡ σ I c / I c ) for 3000 Josephson junctions (both single-junctions and asymmetric SQUIDs) across an area of 49 cm2. Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown σ I c / I c = 1.8% within 1x1 cm, on average, with a few 1x1 cm areas having σ I c / I c < 1.0% (equivalent to σ f / f < 0.5%). Such stability would drastically improve the yield of multi-junction chips with strict critical current requirements.
Flux-tunable transmon incorporating a van der Waals superconductor via an Al/AlOx/4Hb-TaS2 Josephson junction
Incorporating van der Waals (vdW) superconductors into Josephson elements extends circuit-QED beyond conventional Al/AlOx/Al tunnel junctions and enables microwave probes of unconventional condensates and subgap excitations. In this work, we realize a flux-tunable transmon whose nonlinear inductive element is an Al/AlOx/4Hb-TaS2 Josephson junction. The tunnel barrier is formed by sequential deposition and full in-situ oxidation of ultrathin Al layers on an exfoliated 4Hb-TaS2 flake, followed by deposition of a top Al electrode, yielding a robust, repeatable hybrid junction process compatible with standard transmon fabrication. Embedding the device in a three-dimensional copper cavity, we observe a SQUID-like flux-dependent spectrum that is quantitatively reproduced by a standard dressed transmon--cavity Hamiltonian, from which we extract parameters in the transmon regime. Across measured devices we obtain sub-microsecond energy relaxation (T1 from 0.08 to 0.69μs), while Ramsey measurements indicate dephasing faster than our 16 ns time resolution. We also find a pronounced discrepancy between the Josephson energy inferred from spectroscopy and that expected from the Ambegaokar--Baratoff relation using room-temperature junction resistances, pointing to nontrivial junction physics in the hybrid Al/AlOx/4Hb-TaS2 system. Although we do not resolve material-specific subgap modes in the present geometry, this work establishes a practical route to integrating 4Hb-TaS2 into coherent quantum circuits and provides a baseline for future edge-sensitive designs aimed at enhancing coupling to boundary and subgap degrees of freedom in vdW superconductors.
Scaling superconducting quantum processors is fundamentally limited by environmentally induced decoherence arising from nanoscale fabrication defects. Conventional heuristic microwave control protocols cannot dynamically adapt to device-specific material variations, while purely data-driven deep learning approaches often violate physical constraints. Here we introduce a compact quantum physics-informed neural network (QPINN) that learns device-aware microwave control pulses for superconducting qubits. Trained on empirical defect characteristics extracted from 162 InAs nanosheet Josephson junction measurements, the model embeds the Lindblad master equation directly into its loss function to enforce physical consistency. Open-system simulations demonstrate a 42% reduction in leakage to non-computational states. Hardware experiments executed on the 156-qubit IBM Quantum processor show an increase in Ramsey dephasing time from 83.3 ± 7.8 μs to 113.0 ± 1.1 μs while maintaining gate fidelity exceeding 99.99%.