New work on quantum dynamics of regularized superconducting circuits


Image: Sebastian Droege/ Forschungszentrum Jülich


Building a universal quantum computer is a challenging task because physical quantum bits, or qubits, are imperfect. The pursuit of novel qubit designs, which strive for tailored properties such as built-in protection against noise, has led to superconducting circuits that correspond to mechanical systems with constraints. The resulting mechanics of these circuits is not usually rigorously covered in the contemporary literature on circuit quantization. Martin Rymarz and David DiVincenzo analyze in this publication one approach used to describe these circuits quantum mechanically and find that it generally leads to wrong predictions of the system’s dynamics. The work entitled “Consistent Quantization of Nearly Singular Superconducting Circuits” was published on May 1 in Physical Review X (

Specifically, the authors study the quantization of electrical networks that are described mathematically by a noninvertible, or singular, capacitance matrix. A prevalent way to handle such a circuit is to manipulate Kirchhoff’s conservation laws to eliminate variables or change the circuit’s topology. This effectively enforces the underlying constraints and renders the system regular—that is, it is no longer described by a singular matrix—which allows for a conventional quantum-mechanical description.

They compare the results of this process with an effective low-energy analysis of the corresponding regularized circuit that includes nonzero parasitic capacitances, which lift the singularity of the capacitance matrix. A comparison of the dynamics of the singular case and the regularized one reveals that they do not coincide, and we trace back this inconsistency to the absence of quantum fluctuations in the singular theory. Since the regularized description of electrical networks is considered physical, the singular description must be deemed incorrect.

The paper highlights the importance of critically examining the validity of classical network analysis when used in conjunction with circuit quantization. We provide the tools and techniques to effectively handle the quantum dynamics of regularized superconducting circuits near the singular limit.

Consistent Quantization of Nearly Singular Superconducting Circuits
Martin Rymarz and David P. DiVincenzo
Phys. Rev. X 13, 021017 – Published 1 May 2023

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