Circuit complexity of coupled four-mode squeezed states in two-field inflation
Abstract
We study the circuit complexity of coupled curvature and entropy perturbations in two-field inflation. We start from the quadratic action and derive the full Hamiltonian. The Hamiltonian includes all diagonal and off-diagonal quadratic terms. We then obtain three coupled equations for the pair amplitudes of the four-mode squeezed state. From these amplitudes, we calculate the two principal squeezing strengths. We use them to determine the Nielsen circuit complexity. For an equal-weight Gaussian circuit, the complexity takes the form π2,k=β(2(r1k2+r2k2)). It depends on the squeezing strengths but not explicitly on the squeezing angles. Our numerical results show that the complexity grows after horizon crossing in both coupled and uncoupled models. Interfield coupling changes the pair amplitudes and the four-mode squeezed state. However, its effect on the circuit complexity is small for the parameters considered. This result shows that different four-mode pair-amplitude matrices can yield similar values of the chosen equal-weight circuit complexity. The present calculation provides a reference for studying Gaussian circuit complexity in more general two-field inflationary models.
Related
- Circuit Complexity of Scalar and Tensor Perturbations in Luminal Einstein--Gauss--Bonnet Inflation
- Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation
- Deterministic preparation of squeezed and non-Gaussian states in coupled qubit-boson systems
- Coupled quantum critical states in a circuit simulator
- Calculating the squeezed bispectrum in stochastic inflation by Monte Carlo simulation
BibTeX
@misc{li2026circuit,
title = {{Circuit complexity of coupled four-mode squeezed states in two-field inflation}},
author = {Tao Li and Hai-Bing Fu and Lei-Hua Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38254},
eprint = {2610.38254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38254},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Circuit complexity of coupled four-mode squeezed states in two-field inflation
AU - Tao Li
AU - Hai-Bing Fu
AU - Lei-Hua Liu
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38254
UR - https://arxiv.org/abs/2610.38254
AB - We study the circuit complexity of coupled curvature and entropy perturbations in two-field inflation. We start from the quadratic action and derive the full Hamiltonian. The Hamiltonian includes all diagonal and off-diagonal quadratic terms. We then obtain three coupled equations for the pair amplitudes of the four-mode squeezed state. From these amplitudes, we calculate the two principal squeezing strengths. We use them to determine the Nielsen circuit complexity. For an equal-weight Gaussian circuit, the complexity takes the form π_2,k=β(2(r_1k^2+r_2k^2)). It depends on the squeezing strengths but not explicitly on the squeezing angles. Our numerical results show that the complexity grows after horizon crossing in both coupled and uncoupled models. Interfield coupling changes the pair amplitudes and the four-mode squeezed state. However, its effect on the circuit complexity is small for the parameters considered. This result shows that different four-mode pair-amplitude matrices can yield similar values of the chosen equal-weight circuit complexity. The present calculation provides a reference for studying Gaussian circuit complexity in more general two-field inflationary models.
ER -