The increasing size of superconducting quantumcomputer chips requires a shift in evaluation methods for chip design. Three-dimensional (3D) electromagnetic (EM) simulations become computationally intractable as model size increases owing to the exponential growth in computation time. To address this challenge, we develop a technique that analyzes the circuit parameters of large-scale superconducting qubit chips by combining S-parameters simulated in smaller-scale 3D EM models. Herein, we design a four-qubit unit cell for large-scale qubit devices and evaluate both residual qubit-qubit coupling and control-line-to-qubit crosstalk for distant qubit pairs. In addition, we propose guard structures around qubits to mitigate nearestneighbor crosstalk. Although previous methods are limited to chips with at most ten qubits, our approach enables the analysis of systems with over a hundred qubits.
The increasing size of superconducting quantumcomputer chips requires a shift in evaluation methods for chip design. Three-dimensional (3D) electromagnetic (EM) simulations become computationally intractable as model size increases owing to the exponential growth in computation time. To address this challenge, we develop a technique that analyzes the circuit parameters of large-scale superconducting qubit chips by combining S-parameters simulated in smaller-scale 3D EM models. Herein, we design a four-qubit unit cell for large-scale qubit devices and evaluate both residual qubit-qubit coupling and control-line-to-qubit crosstalk for distant qubit pairs. In addition, we propose guard structures around qubits to mitigate nearestneighbor crosstalk. Although previous methods are limited to chips with at most ten qubits, our approach enables the analysis of systems with over a hundred qubits.
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.
Crosstalk between qubits fundamentally limits the scalability of quantum processors, necessitating physics-based models that can handle the complexity of large qubit arrays. Here, we develop a comprehensive theoretical and experimental framework that captures residual interactions between both adjacent and non-adjacent qubits in fixed-frequency transmon lattices. The model integrates the combined effects of exponential localization in banded capacitance matrices, suppression of virtual couplings through detuning products across intermediate modes, and evanescent decay of below-cutoff electromagnetic fields, yielding predictive scaling relations for coupling strength as a function of spatial separation and spectral detuning. Experimental characterization of a 4×4 superconducting-qubit lattice with inductive shunt pillars reveals exponential spatial decay and frequency-dependent suppression consistent with theoretical predictions, achieving quantitative agreement for all nearest-neighbor couplings across the \qtyrange[range-phrase = --, range-units = single]{4}{6}{\giga\hertz} operating range. Our results show that standard dispersive Hamiltonian approximations systematically overestimate long-range coupling when spatial and spectral dependencies are neglected; these errors propagate into circuit simulation and design strategies. Our framework provides design guidance for crosstalk mitigation in larger-scale quantum processors under realistic fabrication constraints, addressing a bottleneck in scalability.
To demonstrate supremacy of quantum computing, increasingly large-scale superconducting quantum computing chips are being designed and fabricated. However, the complexity of simulating quantum systems poses a significant challenge to computer-aided design of quantum chips, especially for large-scale chips. Harnessing the scalability of graph neural networks (GNNs), we here propose a parameter designing algorithm for large-scale superconducting quantum circuits. The algorithm depends on the so-called "three-stair scaling" mechanism, which comprises two neural-network models: an evaluator supervisedly trained on small-scale circuits for applying to medium-scale circuits, and a designer unsupervisedly trained on medium-scale circuits for applying to large-scale ones. We demonstrate our algorithm in mitigating quantum crosstalk errors. Frequencies for both single- and two-qubit gates (corresponding to the parameters of nodes and edges) are considered simultaneously. Numerical results indicate that the well-trained designer achieves notable advantages in efficiency, effectiveness, and scalability. For example, for large-scale superconducting quantum circuits consisting of around 870 qubits, our GNNs-based algorithm achieves 51% of the errors produced by the state-of-the-art algorithm, with a time reduction from 90 min to 27 s. Overall, a better-performing and more scalable algorithm for designing parameters of superconducting quantum chips is proposed, which demonstrates the advantages of applying GNNs in superconducting quantum chips.
Abstract The arithmetic power of a quantum computer is determined by a combination of the number of quantum bits and the fidelity of a single bit. Superconducting quantum chips can be prepared using a process similar to that of semiconductor chips, and are therefore of interest because of their natural advantages in terms of scalability. However, as the number of quantum bits increases, the z-control lines (magnetic field control lines) on the superconducting quantum chip also increase, leading to increased magnetic field crosstalk between individual control lines, which affects the fidelity of a single bit and further affects the arithmetic power of superconducting quantum computing. To address the above problems, this paper proposes two methods to reduce the magnetic field crosstalk between the control lines by modeling and simulating the superconducting quantum chip using air bridges and inflow structures, and the simulation results show that the magnetic field crosstalk between the control lines is significantly improved after the introduction of air bridges and inflow structures. This work provides a basis for further suppression of magnetic field crosstalk between the z-control lines of superconducting quantum chips.
Superconducting qubits are one of the most mature platforms for achieving practical quantum computers, but significant performance improvements are still needed. To improve the engineering of these systems, three-dimensional (3D) full-wave computational electromagnetics analyses are increasingly being turned to. Unfortunately, existing analysis approaches often rely on full-wave simulations using eigenmode solvers that are typically cumbersome, not robust, and computationally prohibitive if devices with more than a few qubits are to be analyzed. To improve the characterization of superconducting circuits while circumventing these drawbacks, this work begins the development of an alternative modeling framework that we illustrate in the context of evaluating the qubit-qubit exchange coupling rate between transmon qubits. This quantity is a key design parameter that determines the entanglement rate for fast multiqubit gate performance and also affects decoherence sources like qubit crosstalk. Our modeling framework uses a field-based formalism in the context of macroscopic quantum electrodynamics, which we use to show that the qubit-qubit exchange coupling rate can be related to the electromagnetic dyadic Green's function linking the qubits together. We further show how the needed quantity involving the dyadic Green's function can be related to the impedance response of the system that can be easily and efficiently computed with classical computational electromagnetics tools. We demonstrate the validity and efficacy of this approach by simulating four practical multiqubit superconducting circuits and evaluating their qubit-qubit exchange coupling rates. We validate our results against a 3D numerical diagonalization method and against experimental data where available. We also demonstrate the impact of the qubit-qubit exchange coupling rate on qubit crosstalk by simulating a multicoupler device and identifying operating points where the qubit crosstalk becomes zero.
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%.