Optimal intermediate or mode-dependent gauge selection

Determine which intermediate or mode-dependent gauge provides the most accurate finite-order effective truncation for superconducting circuit environments beyond the two canonical charge and flux gauges.

Background

The paper derives exact Hamiltonians in two endpoint gauges: the charge gauge for impedance descriptions and the flux gauge for admittance descriptions. These gauges produce diagonal dressed environmental sectors and divergence-free reduced models, but intermediate or mode-dependent canonical transformations may yield more accurate finite-order approximations in particular parameter regimes.

The authors explicitly identify the general optimization of this gauge choice as unresolved, especially when constructing dispersive effective Hamiltonians or reduced models for systems with different coupling strengths and spectral structures.

References

We restrict these reductions to the two extreme gauges, although intermediate or mode-dependent gauges may be advantageous in specific regimes, with their optimal choice remaining open.

— Immittance formulas for exact blackbox quantization and divergence-free effective models in circuit QED  (2608.26027 - Gigon et al., 26 Aug 2026) in Introduction, paragraph beginning “Spectrally resolved environments yield dispersive effective Hamiltonians”; also discussed in Section 2

Determining which effective frame provides the more accurate truncation more generally remains an open question.

— Immittance formulas for exact blackbox quantization and divergence-free effective models in circuit QED  (2608.26027 - Gigon et al., 26 Aug 2026) in Section 3, immediately after Eq. (DiscreteGeneralCouplingMain)