A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study

Taha Rajabzadeh; Alex Boulton-McKeehan; Sam Bonkowsky; David I. Schuster; Amir H. Safavi-Naeini

doi:10.22331/q-2026-10-27-2249

A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study

Taha Rajabzadeh¹, Alex Boulton-McKeehan², Sam Bonkowsky³, David I. Schuster², and Amir H. Safavi-Naeini²

¹Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
²E. L. Ginzton Laboratory and the Department of Applied Physics, Stanford University, Stanford, CA 94305 USA
³Department of Physics, Stanford University, Stanford, CA 94305 USA

Published:	2026-10-27, volume 10, page 2249
Editor:	Jens Siewert
Eprint:	arXiv:2408.12704v3
Doi:	https://doi.org/10.22331/q-2026-10-27-2249
Citation:	Quantum 10, 2249 (2026).

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Abstract

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of eigenvalues and eigenvectors of a Hamiltonian–a large, sparse matrix–relative to system properties poses a significant challenge, especially for arbitrary systems. Superconducting quantum circuits offer substantial flexibility in Hamiltonian design, making them an ideal platform for this task. In this work, we present a comprehensive framework for the gradient-based optimization of superconducting quantum circuits, leveraging the SQcircuit software package. By addressing the challenge of calculating the gradient of the eigensystem for large, sparse Hamiltonians and integrating automatic differentiation within SQcircuit, our framework enables efficient and precise computation of gradients for various circuit properties or custom-defined metrics, streamlining the optimization process. We apply this framework to the qubit discovery problem, demonstrating its effectiveness in identifying qubit designs with superior performance metrics. The optimized circuits show improvements in a heuristic measure of gate count, upper bounds on gate speed, decoherence time, and resilience to noise and fabrication errors compared to existing qubits. While this methodology is showcased through qubit optimization and discovery, it is versatile and can be extended to tackle other optimization challenges in superconducting quantum hardware design.

Popular summary

One promising approach to scalable quantum computing involves using superconducting quantum circuits. A key feature of these systems is that their Hamiltonian can be manipulated by engineering macroscopic parameters such as capacitance, inductance, and circuit topology. Given this flexibility, finding circuit designs which exhibit optimal performance as qubits or for other tasks remains an open problem. Here, we introduce a software framework to optimize, using gradient-based methods, any superconducting circuit for arbitrary target behavior.

As an initial target, we apply this framework towards finding circuits with improved performance as qubits. To this end, we demonstrate effective optimization for metrics such as coherence time and gate speed, while enforcing hardware constraints including sensitivity to certain noise channels and nanofabrication variability. Performing an exhaustive search over a class of simple "single-loop" circuits with realistic parameter values, we find that fluxonium circuits (consisting of a superinductor and single Josephson junction) perform best among the circuit types we consider. Moreover, the best results from our automated optimization routine exceed simulated results from contemporary qubit designs in the literature in estimated gate count, while satisfying our constraints on noise and fabrication sensitivity.

We have oriented our approach to develop experimentally realistic designs, and hope to use this strategy to create better devices for future laboratory tests. Additionally, our framework, available in the open-source SQcircuit software package, can be applied to many other design tasks. We see potential for this approach across a broad class of problems, including hardware-aware quantum control, error correction, and quantum sensing.

► BibTeX data

@article{Rajabzadeh2026generalframework,
  doi = {10.22331/q-2026-10-27-2249},
  url = {https://doi.org/10.22331/q-2026-10-27-2249},
  title = {A {G}eneral {F}ramework for {G}radient-{B}ased {O}ptimization of {S}uperconducting {Q}uantum {C}ircuits using {Q}ubit {D}iscovery as a {C}ase {S}tudy},
  author = {Rajabzadeh, Taha and Boulton-McKeehan, Alex and Bonkowsky, Sam and Schuster, David I. and Safavi-Naeini, Amir H.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2249},
  month = oct,
  year = {2026}
}

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[7] E. Palumbo, A. Alocco, A. Celotto, L. Fasolo, B. Galvano, P. Livreri, and E. Enrico, "JCO: Optimization Framework for Nonlinear Superconducting Circuits Using a Lumped-Element Approach and Harmonic Balance", IEEE Transactions on Applied Superconductivity 36 5, TASC.2026 (2026).

[8] Nicolas Wittler, Shai Machnes, and Frank K. Wilhelm, "Co-designing Transmon devices for control with simple pulses", arXiv:2410.13619, (2024).

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