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Apress eBooks

Superconducting Qubit Design Using Qiskit Metal

Subhojit Halder, Kinjal A. Chauhan, Muhamad Bagher Barfar, Srinjoy Ganguly, Shalini Devendrababu

Published Jan 1, 2025• 1 citation
Publisher

Abstract

This book provides practical knowledge and step-by-step guidance on designing, analyzing, and fabricating quantum chips.
DOI
10.1007/979-8-8688-1504-1

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Quantum computing is advancing rapidly, with superconducting quantum computing (SQC) emerging as one of the most promising platforms for scalable quantum information processing. In contrast to fabrication-focused approaches prevalent in current literature, this work presents a fully simulation-based design and tuning methodology for a small-scale superconducting quantum chip - addressing practical limitations posed by fabrication resource constraints - and consequently excludes physical chip fabrication or real-time performance evaluation (e.g., fidelity and error rate measurements). A meticulous, step-by-step electromagnetic simulation was conducted on the chip, designed using Qiskit Metal and Ansys Electronics, with qubit parameters tuned and verified using the Lumped Oscillator Model (LOM) and Energy Participation Ratio (EPR) methods. The design achieves good parameter convergence with relative tuning error rates (Δ%) below 0.05% after 15 adaptive passes and approximately 50,000 solved mesh elements, yielding an Energy Participation Ratio (EPR) of 91.8 % for the chip substrate (Silicon). Furthermore, the study includes a theoretical comparison between two fundamental qubit-qubit coupling schemes. A key contribution of this work lies in systematically analyzing how geometric variations in qubit design affect critical quantum parameters such as qubit frequencies, anharmonicities, coupling strengths, and dispersive shifts - thereby offering a comprehen-sive, simulation-driven framework for early-stage quantum chip prototyping.

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Qiskit Metal and Introduction to Chip Design

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As discussed in previous chapters, the Qiskit Metal framework plays a crucial role in designing superconducting qubits. Moving forward, we will use this framework extensively for simulations, where we’ll need to code specific parameters to generate simulations, matrices, and desired outputs. The framework is built using the Python programming language, and Qiskit Metal supports a Python IDE, which facilitates efficient coding. In this chapter, we will explore how to write Python code to develop superconducting circuits. However, before diving directly into the code for superconducting qubits, it is essential to understand some basic concepts.

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This paper presents an electromagnetic-to-Hamiltonian workflow for modeling a two-qubit coupled transmon superconducting device circuit. The device layout, comprising two coupled transmon qubits with individual readout resonators, is designed and parameterized in Qiskit Metal and analyzed using 3D eigenmode simulations in Ansys HFSS. Adaptive-pass refinement converges the eigenfrequencies and electromagnetic fields, yielding reliable modal data for quantization. Energy-participation ratio values from HFSS are processed through the pyEPR–Qiskit Metal flow to extract effective capacitances, anharmonicities, and qubit–resonator couplings. These parameters define a multimode Duffing–Jaynes–Cummings Hamiltonian that captures the transmon nonlinearities and their interactions with the resonator modes. Frequency-convergence checks and coupling diagnostics verify a consistent, physically accurate mapping from the layout geometry to the device circuit-level model. The Hamiltonian workflow offers a reproducible and scalable framework for modeling and analyzing superconducting transmon architectures in quantum chip design.

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Springer eBooks•Jan 1, 2025•0 citations
Quantum computing is advancing rapidly, with superconducting quantum computing (SQC) emerging as one of the most promising platforms for scalable quantum information processing. In contrast to fabrication-focused approaches prevalent in current literature, this work presents a fully simulation-based design and tuning methodology for a small-scale superconducting quantum chip - addressing practical limitations posed by fabrication resource constraints - and consequently excludes physical chip fabrication or real-time performance evaluation (e.g., fidelity and error rate measurements). A meticulous, step-by-step electromagnetic simulation was conducted on the chip, designed using Qiskit Metal and Ansys Electronics, with qubit parameters tuned and verified using the Lumped Oscillator Model (LOM) and Energy Participation Ratio (EPR) methods. The design achieves good parameter convergence with relative tuning error rates (Δ%) below 0.05% after 15 adaptive passes and approximately 50,000 solved mesh elements, yielding an Energy Participation Ratio (EPR) of 91.8 % for the chip substrate (Silicon). Furthermore, the study includes a theoretical comparison between two fundamental qubit-qubit coupling schemes. A key contribution of this work lies in systematically analyzing how geometric variations in qubit design affect critical quantum parameters such as qubit frequencies, anharmonicities, coupling strengths, and dispersive shifts - thereby offering a comprehen-sive, simulation-driven framework for early-stage quantum chip prototyping.
As discussed in previous chapters, the Qiskit Metal framework plays a crucial role in designing superconducting qubits. Moving forward, we will use this framework extensively for simulations, where we’ll need to code specific parameters to generate simulations, matrices, and desired outputs. The framework is built using the Python programming language, and Qiskit Metal supports a Python IDE, which facilitates efficient coding. In this chapter, we will explore how to write Python code to develop superconducting circuits. However, before diving directly into the code for superconducting qubits, it is essential to understand some basic concepts.
This paper presents an electromagnetic-to-Hamiltonian workflow for modeling a two-qubit coupled transmon superconducting device circuit. The device layout, comprising two coupled transmon qubits with individual readout resonators, is designed and parameterized in Qiskit Metal and analyzed using 3D eigenmode simulations in Ansys HFSS. Adaptive-pass refinement converges the eigenfrequencies and electromagnetic fields, yielding reliable modal data for quantization. Energy-participation ratio values from HFSS are processed through the pyEPR–Qiskit Metal flow to extract effective capacitances, anharmonicities, and qubit–resonator couplings. These parameters define a multimode Duffing–Jaynes–Cummings Hamiltonian that captures the transmon nonlinearities and their interactions with the resonator modes. Frequency-convergence checks and coupling diagnostics verify a consistent, physically accurate mapping from the layout geometry to the device circuit-level model. The Hamiltonian workflow offers a reproducible and scalable framework for modeling and analyzing superconducting transmon architectures in quantum chip design.