We present the analysis of 3D superconducting qubits using PathWave EMPro with its scripting feature that enables quantum parameter extraction and design automation of 3D qubits. In the electromagnetic study, the qubits are represented by their ‘linearized’ lumped inductances at very low signal excitation, and then for a full description of the quantum system, the nonlinear quantum parameters are extracted. We consider here the configuration in Ref. [1] as a showcase example of a 3D qubit with published measurements. Qubit anharmonicities and cross-Kerr strengths are calculated from both the frequency domain response using black-box quantization [2] and from the eigenmode solution using the energy participation method [3], [4]. For a rigorous nonlinear analysis, the frequency response of the 3D qubit using a nonlinear Josephson junction model is produced in PathWave ADS Co-simulation environment. Both the linear and nonlinear analyses in PathWave tools yield similar circuit responses, which validate the accuracy of EMPro to simulate 3D superconducting qubits.
We present the analysis of 3D superconducting qubits using PathWave EMPro with its scripting feature that enables quantum parameter extraction and design automation of 3D qubits. In the electromagnetic study, the qubits are represented by their ‘linearized’ lumped inductances at very low signal excitation, and then for a full description of the quantum system, the nonlinear quantum parameters are extracted. We consider here the configuration in Ref. [1] as a showcase example of a 3D qubit with published measurements. Qubit anharmonicities and cross-Kerr strengths are calculated from both the frequency domain response using black-box quantization [2] and from the eigenmode solution using the energy participation method [3], [4]. For a rigorous nonlinear analysis, the frequency response of the 3D qubit using a nonlinear Josephson junction model is produced in PathWave ADS Co-simulation environment. Both the linear and nonlinear analyses in PathWave tools yield similar circuit responses, which validate the accuracy of EMPro to simulate 3D superconducting qubits.
We present current developments in Keysight Pathwave Quantum Technology to analyze superconducting quantum circuits. Particularly, Pathwave ADS and its most recent Electromagnetic (EM) simulation package, QuantumPro, enable investigating nonlinear effects such as cavity quantum electrodynamics and automated computation of the quantum parameters including the qubit anharmonicities and cross-Kerr strengths. Under the low power assumption, superconducting qubits are treated as linear lumped circuit elements in the EM simulation environment. To study the nonlinear regime, Pathwave ADS provides a co-simulation approach that enables combining the linear frequency response from the full-wave EM simulation with the nonlinear circuit analysis in the ADS schematic. To assess the accuracy of Pathwave ADS, we compare the results to the two coupled transmons showcase example from the IBM Quantum Qiskit Metal framework. In addition, we also demonstrate power-dependent nonlinear bending of the frequency response by sweeping the input power into the superconducting circuits in Pathwave ADS.
This work presents a comprehensive analytical and simulation-based study of superconducting quantum chip architectures, spanning both 2D planar and 3D-integrated designs. We first design and simulate a planar quantum chip layout using Qiskit Metal, which is imported into Ansys HFSS (High Frequency Structure Simulator) to construct a 3D model and perform electromagnetic simulations. A detailed analysis using Driven Modal, Eigenmode, Magnetostatic, and Q3D Capacitance Extraction solvers ensures our simulations accurately reflect physical behavior. The results are validated against analytical models from microwave engineering. pyEPR (Python Energy Participation Ratio) is used to extract key quantum metrics, including eigenfrequencies, quality factors, decoherence times, anharmonicity, cross-Kerr interactions, and participation ratios. Building on this planar design, we extend our study to a 3D-integrated flip-chip architecture featuring two superconducting qubits fabricated on separate high-resistivity silicon substrates. Using HFSS and analytical modeling, we show that detuned qubits maintain stable eigenfrequencies, quality factors, decoherence times, anharmonicity, and cross-Kerr interactions over varying substrate separation values. However, the introduction of dielectric loss tangents reduces quality factors which degrades coherence times and introduces an additional dephasing. These findings highlight the potential of 3D quantum integration, given minimal material imperfections.The planar and 3D designs together form a cohesive investigation into next-generation quantum hardware, with the 2D layout currently taped-out and under fabrication.
Optimizing the performance of cryogenic quantum amplifiers is a key step toward achieving high-fidelity and scalable qubit readout. In this work, we present efficient and accurate modeling of a Josephson traveling-wave parametric amplifier (JTWPA) based on electromagnetic (EM) and circuit co-simulation. In contrast to conventional simulation methods where an equivalent lumped-element circuit model of the JTWPA is required, we directly perform full EM analysis of the device to faithfully determine the linear response. The extracted S-parameters are then fed into a nonlinear harmonic balance simulator with Josephson junctions represented as circuit elements. The simulated linear and gain properties are compared with experimental results and show good agreement.
In the design of superconducting quantum chips, the control and readout of the quantum bit (qubit) are realized through interactions with other components in the circuit, such as drive lines, flux lines and readout resonator. Depending on the design, these interactions employ either an inductive or capacitive coupling scheme. Note that every interaction governs critical performance metrics for the chip, including gate fidelity, readout speed, and coherence times, a more effective and precise approach to extract the strength of the coupling is necessary. For most qubit designs, the structure of the qubit typically remains in the electrically small regime. Therefore, simulation software based on static fields and the Method of Moments (MoM), such as Q3D, is still applicable in most instances. However, as the number of qubits on a chip increases, Q3D faces challenges in effectively addressing the complex coupling and crosstalk issues present on the chip. In this work, we extend the lumped-element-based qubit model by using microwave network parameters and thus enable the simulation of the qubit for the Finite Element Method (FEM)-based 3D electromagnetic simulation software, such as HFSS. This approach is suitable for the determination of the capacitive coupling strength between the qubit and the drive line, as well as readout circuits. Furthermore, to address the inductive coupling between the qubit and the flux line, we propose a method in this work that directly computes the mutual inductance, which is implemented by determining the magnetic flux through the DC SQUID area, generated by the current port excitation in HFSS. The proposed methodologies not only effectively extracts the key qubit design parameters, but also offer broader applicability for analysing complex crosstalk in multi-qubit chip designs.
We present a method for the numerical analysis of superconducting quantum circuits combining lumped elements, either linear or nonlinear (i.e., Josephson junctions), and distributed coplanar waveguide (CPW) structures. CPW transmission lines and multiline couplers are directly modeled without discretizing them into lumped-element equivalents, and the circuit Hamiltonian parameters are extracted by using the energy-participation ratio (EPR) method. This approach enables fast and accurate extraction of mode frequencies, anharmonicities, cross-Kerr interactions, and Purcell decay rates without relying on full electromagnetic simulations, while naturally accounting for higher-order modes of distributed components. We have implemented the proposed method in a Python framework, QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), which we have used to validate the approach against full electromagnetic simulations (Ansys HFSS, pyEPR), existing circuit-analysis tools (QuCAT), and designs reported in the literature. The comparisons show excellent agreement with orders-of-magnitude reductions in computational time relative to full-wave solvers. We demonstrate applications including Purcell-protected readout, multimode ultrastrong coupling, and multiplexed qubit readout, illustrating how the method can support fast and reliable early-stage circuit design.
High-fidelity control of superconducting quantum processors requires accurate characterization of electromagnetic coupling strengths among the device's constituent elements. Accurately extracting these couplings across large-scale architectures, presently featuring hundreds of qubits, poses a challenging multi-scale modeling problem. This requires resolving scales from the nanometer-scale geometry of Josephson junctions and their leads to the centimeter-scale size of the enclosing metallic packages. We present four numerical coupling extraction methods based on the avoided level crossing, the energy participation ratio, the induced electromotive force, and the impedance matrix. These methods are tailored to work with commercially available 3D electromagnetic solvers. We benchmark these techniques on a 10×10 array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.