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  • Open Access

Circuit quantization from first principles

Yun-Chih Liao1,2,*, Ben J. Powell2, and Thomas M. Stace1,2,†

  • *Contact author: uqyliao1@uq.edu.au
  • †Contact author: stace@physics.uq.edu.au
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Phys. Rev. Research 7, 033144 – Published 11 August, 2025

DOI: https://doi.org/10.1103/dfrq-44vk

Abstract

Superconducting circuit quantization conventionally starts from classical Euler-Lagrange circuit equations of motion. Invoking the correspondence principle yields a canonically quantized description of circuit dynamics over a bosonic Hilbert space. This approach has been very successful for describing experiments, but implicitly starts from the classical Ginsberg-Landau mean-field theory for the circuit. Here, we employ a different approach that starts from a microscopic fermionic Hamiltonian for interacting electrons, whose ground space is described by the Bardeen-Cooper-Schrieffer (BCS) many-body wave function that underpins conventional superconductivity. We introduce the BCS ground space as a subspace of the full fermionic Hilbert space, and show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for Josephson junctions, capacitors, and inductors, from which standard quantized circuit models follow. This approach does not impose a spontaneously broken symmetry so that it consistently describes quantized circuits that support superpositions of phases, and the canonical commutation relations between phase and charge are derived from the underlying fermionic commutation properties, rather than imposed. By expanding the projective subspace, this approach can be extended to describe phenomena outside the BCS ground space, including quasiparticle excitations.

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Phys. Rev. Research 7, 033144– Published 11 August, 2025
  • Received 19 January 2025
  • Accepted 14 July 2025
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