Which Superconducting Qubit Model is Good Enough? From Effective Two-Level to Circuit-Based Hamiltonians for Pulse-Level Simulation

2026-05-21

AI Summary

This study addresses the challenge of balancing model accuracy and computational cost in pulse-level simulation of superconducting quantum hardware. Focusing on flux-tunable two-qubit systems, the authors conduct a unified benchmark of three Hamiltonian models—effective two-level, three-mode Duffing, and circuit-level charge-basis transmon—evaluating their performance in static spectra, qubit interactions, driven dynamics, CZ gate fidelity, and leakage. The results demonstrate that the Duffing model significantly outperforms the effective model in capturing static and coupling characteristics, while multi-level effects reveal driven behaviors inaccessible to the latter. Based on these findings, the work proposes a hierarchical modeling strategy: using the effective model for rapid analysis, the Duffing model as the default multi-level tool, and the full circuit model for high-fidelity validation, thereby offering practical guidance for efficient yet accurate simulation.

Abstract

Pulse-level simulators are the lowest-level, most widely used abstraction layer for studying how quantum hardware responds to control signals, but they can be built on Hamiltonian models with very different fidelity and cost. This raises the question: which level of physical abstraction is sufficient for a given simulation objective? We study this question for a flux-tunable two-qubit superconducting device with a fixed bus coupler by comparing three Hamiltonian descriptions of the same hardware: an effective two-level model, a three-mode Duffing model, and a circuit-based transmon model in the charge basis. Using a realistic parameter set, we evaluate these models on a common benchmark suite spanning flux-dependent spectra, extracted two-qubit interaction terms, driven single-qubit dynamics, CZ gate dynamics, leakage outside the computational subspace, and runtime. Across the tested flux range, the Duffing model follows the circuit-based reference more closely than the effective model for static spectra and reduced two-qubit quantities, while in driven benchmarks, the multilevel models reveal effects absent in the effective description. Overall, the results support a layered use of abstraction in pulse-level simulation: effective models for reduced analyses, Duffing models as a practical multilevel default, and circuit-based models for high-fidelity reference simulation or detailed leakage analysis.

Problem

• superconducting qubit
• pulse-level simulation
• Hamiltonian model
• model fidelity
• abstraction level

Innovation

• pulse-level simulation
• superconducting qubit
• Hamiltonian modeling
• Duffing oscillator
• circuit quantization