Analysis of arbitrary superconducting quantum circuits accompanied by a Python package: SQcircuit

Taha Rajabzadeh1, Zhaoyou Wang2, Nathan Lee2, Takuma Makihara2, Yudan Guo2, 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

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Superconducting quantum circuits are a promising hardware platform for realizing a fault-tolerant quantum computer. Accelerating progress in this field of research demands general approaches and computational tools to analyze and design more complex superconducting circuits. We develop a framework to systematically construct a superconducting quantum circuit's quantized Hamiltonian from its physical description. As is often the case with quantum descriptions of multicoordinate systems, the complexity rises rapidly with the number of variables. Therefore, we introduce a set of coordinate transformations with which we can find bases to diagonalize the Hamiltonian efficiently. Furthermore, we broaden our framework's scope to calculate the circuit's key properties required for optimizing and discovering novel qubits. We implement the methods described in this work in an open-source Python package $\tt{SQcircuit}$. In this manuscript, we introduce the reader to the $\tt{SQcircuit}$ environment and functionality. We show through a series of examples how to analyze a number of interesting quantum circuits and obtain features such as the spectrum, coherence times, transition matrix elements, coupling operators, and the phase coordinate representation of eigenfunctions.

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Cited by

[1] Zhaoyou Wang and Amir H. Safavi-Naeini, "Quantum control and noise protection of a Floquet 0−π qubit", Physical Review A 109 4, 042607 (2024).

[2] Nathan R.A. Lee, Yudan Guo, Agnetta Y. Cleland, E. Alex Wollack, Rachel G. Gruenke, Takuma Makihara, Zhaoyou Wang, Taha Rajabzadeh, Wentao Jiang, Felix M. Mayor, Patricio Arrangoiz-Arriola, Christopher J. Sarabalis, and Amir H. Safavi-Naeini, "Strong Dispersive Coupling Between a Mechanical Resonator and a Fluxonium Superconducting Qubit", PRX Quantum 4 4, 040342 (2023).

[3] Andrew Osborne, Trevyn Larson, Sarah Garcia Jones, Ray W. Simmonds, András Gyenis, and Andrew Lucas, "Symplectic Geometry and Circuit Quantization", PRX Quantum 5 2, 020309 (2024).

[4] A. Parra-Rodriguez and I. L. Egusquiza, "Geometrical description and Faddeev-Jackiw quantization of electrical networks", arXiv:2304.12252, (2023).

[5] I. L. Egusquiza and A. Parra-Rodriguez, "Algebraic canonical quantization of lumped superconducting networks", Physical Review B 106 2, 024510 (2022).

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