SuperGrad: a differentiable simulator for superconducting processors

Ziang Wang; Feng Wu; Hui-Hai Zhao; Xin Wan; Xiaotong Ni

doi:10.22331/q-2025-04-24-1722

SuperGrad: a differentiable simulator for superconducting processors

Ziang Wang¹, Feng Wu², Hui-Hai Zhao², Xin Wan¹, and Xiaotong Ni³

¹Zhejiang Institute of Modern Physics and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Zhejiang University, Hangzhou 310027, China
²Zhongguancun Laboratory, Beijing, China
³Quantum Science Center of Guangdong-Hong Kong-Macao, Shenzhen 518045, China

Published:	2025-04-24, volume 9, page 1722
Editor:	Dan Browne
Eprint:	arXiv:2406.18155v3
Doi:	https://doi.org/10.22331/q-2025-04-24-1722
Citation:	Quantum 9, 1722 (2025).

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Abstract

One significant advantage of superconducting processors is their extensive design flexibility, which encompasses various types of qubits and interactions. Given the large number of tunable parameters of a processor, the ability to perform gradient optimization would be highly beneficial. Efficient backpropagation for gradient computation requires a tightly integrated software library, for which no open-source implementation is currently available. In this work, we introduce SuperGrad, a simulator that accelerates the design of superconducting quantum processors by incorporating gradient computation capabilities. SuperGrad offers a user-friendly interface for constructing Hamiltonians and computing both static and dynamic properties of composite systems. This differentiable simulation is valuable for a range of applications, including optimal control, design optimization, and experimental data fitting. In this paper, we demonstrate these applications through examples and code snippets.

Featured image: Sketch of a chain-like fluxonium quantum processor with fluxonium qubits biased at the sweetspot, and multipath coupling is used between neighboring qubit pairs. (a) The fluxonium 3-qubit chain arranged in a frequency pattern is highlighted in the red rectangle. Microwave pulses manipulate the gray qubit via its flux drive. (b) 10-qubit chain-like quantum processor with simultaneous gate control. The fluxonium qubits are periodically arranged in a 3-qubit chain pattern, while their parameters have additional small deviations.

The code is available here.

Popular summary

SuperGrad, a differentiable simulator for superconducting quantum processors, is written in Python and offers a simple and intuitive interface for describing various types of superconducting qubits and their interactions. By also providing information about qubit control and the desired objective function, the library can efficiently compute the gradients with respect to the processor and control parameters through backpropagation.

Intuitively, the gradients contain information about how each parameter should be changed to improve the processors, and this is the idea behind various optimizers based on gradient descent. In general, the multiplicative speedup achieved by using backpropagation to compute the gradients is proportional to the number of parameters. Therefore, for a time-consuming simulation with dozens of parameters, backpropagation can offer a decent multiplicative speedup and potentially a very large absolute speedup.

After the gradients are computed, they can help us perform joint optimization of these parameters, which is beneficial because these parameters can be heavily intertwined in the Hamiltonian. The efficient gradient computation is a result of considering the simulation from constructing superconducting qubits to dynamics as a whole. Our library can be viewed as a combination of previous libraries, such as SCQubits and Qiskit Dynamics. However, since they each focus on a specific part of the simulation, they cannot perform backpropagation of gradients between them.

As a versatile library, SuperGrad is specifically designed for the simulation and optimization of quantum processors. SuperGrad seamlessly integrates the quantum processor device and control optimization within a gradient-based framework. In this work, we show that the Trotterization solver serves as an efficient differentiable time evolution engine. With the help of SuperGrad's components, users can easily simulate their quantum processors, even with novel gate schemes. We want to emphasize that SuperGrad supports a wide range of gate schemes and is not limited to the specific showcases presented in this article. Our SuperGrad library is open source on GitHub, it is continually evolving to meet the escalating demands for simulating larger quantum processors.

► BibTeX data

@article{Wang2025supergrad,
  doi = {10.22331/q-2025-04-24-1722},
  url = {https://doi.org/10.22331/q-2025-04-24-1722},
  title = {Super{G}rad: a differentiable simulator for superconducting processors},
  author = {Wang, Ziang and Wu, Feng and Zhao, Hui-Hai and Wan, Xin and Ni, Xiaotong},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1722},
  month = apr,
  year = {2025}
}

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[1] A. S. Naumov and V. Yu. Popov, "Reconstruction of a Time-Dependent Quantum Hamiltonian Using Neural Differential Equations", Moscow University Physics Bulletin 81 1, 30 (2026).

[2] A.S. Naumov and V.Yu. Popov, "Reconstruction of a Time-Dependent Quantum Hamiltonian Using Neural Differential Equations", Vestnik Moskovskogo Universiteta Seriya 3 Fizika Astronomiya 2026-1, 2610103 (2025).

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