Instantaneous-Frame Theory of Strongly Driven Parametric Gates
Abstract
Parametric two-qubit gates using tunable couplers are a promising approach to scalable superconducting quantum processors. However, conventional theories formulated in the idle eigenbasis break down in the large-amplitude regime required for fast gate operations. Here, we show that parametric gates are more naturally and accurately described as coherent rotations between instantaneous eigenstates rather than idle eigenstates. This approach may appear counterintuitive, since instantaneous eigenbases are usually associated with adiabatic dynamics. However, they also form a natural moving frame for driven dynamics, where the non-Abelian Berry connection governs transitions and provides a compact description of the exchange and effective ZZ couplings. We show that this theory achieves quantitative agreement with exact numerical simulations across representative tunable-coupler architectures, including double-transmon, capacitively shunted double-transmon, and single-transmon couplers. The description remains accurate even in regimes where idle-frame descriptions fail, while substantially reducing the reliance on computationally demanding exact simulations. These results establish an instantaneous-frame theory of parametric gates beyond conventional idle-frame models and provide a new perspective on driven quantum dynamics.
Related
- Heat transport in driven quantum systems: Comparison between the Floquet-Redfield equation and the master equation in the instantaneous eigenbasis
- Frame dependence of heavy-quark observables in a rotating strongly coupled plasma
- Lagrangian Dynamical Theory of the Velocity Gradient Tensor: Real Schur Form, Schur Frame, Characteristic Vorticity Modes, and Commutative Vorticity Operators
- From weakly to strongly-interacting driven-dissipative bosons in one dimension
- Emergence of nonequilibrium Lieb excitations in periodically-driven strongly-interacting bosons
BibTeX
@misc{kubo2026instantaneousframe,
title = {{Instantaneous-Frame Theory of Strongly Driven Parametric Gates}},
author = {Kentaro Kubo and Shinichi Inoue and Jushin Tei and Yinghao Ho and Yasunobu Nakamura and Hayato Goto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08348},
eprint = {2609.08348},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08348},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Instantaneous-Frame Theory of Strongly Driven Parametric Gates
AU - Kentaro Kubo
AU - Shinichi Inoue
AU - Jushin Tei
AU - Yinghao Ho
AU - Yasunobu Nakamura
AU - Hayato Goto
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08348
UR - https://arxiv.org/abs/2609.08348
AB - Parametric two-qubit gates using tunable couplers are a promising approach to scalable superconducting quantum processors. However, conventional theories formulated in the idle eigenbasis break down in the large-amplitude regime required for fast gate operations. Here, we show that parametric gates are more naturally and accurately described as coherent rotations between instantaneous eigenstates rather than idle eigenstates. This approach may appear counterintuitive, since instantaneous eigenbases are usually associated with adiabatic dynamics. However, they also form a natural moving frame for driven dynamics, where the non-Abelian Berry connection governs transitions and provides a compact description of the exchange and effective ZZ couplings. We show that this theory achieves quantitative agreement with exact numerical simulations across representative tunable-coupler architectures, including double-transmon, capacitively shunted double-transmon, and single-transmon couplers. The description remains accurate even in regimes where idle-frame descriptions fail, while substantially reducing the reliance on computationally demanding exact simulations. These results establish an instantaneous-frame theory of parametric gates beyond conventional idle-frame models and provide a new perspective on driven quantum dynamics.
ER -