Quantum Simulation of Strongly Correlated Fermion–Phonon Models in Circuit QED

This paper addresses the challenge of simulating electron-phonon (e-ph) models on quantum hardware. Traditional qubit-only simulators struggle with bosonic degrees of freedom due to the high overhead of finite-dimensional encodings. The authors propose a digital-analog circuit QED architecture that maps fermions to transmon qubits and bosons directly to microwave resonators. The core of this approach is a qubit-resonator Rabi gate, which is constructed by interleaving resonant Jaynes-Cummings gates with single-qubit rotations. This gate serves as the fundamental building block for simulating complex many-body systems.

The authors demonstrate how this Rabi gate can be used to construct quantum circuits for the Hubbard-Holstein (HH) model and the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model. For the HH model, they develop a hardware-oriented variational Hamiltonian ansatz (VHA) for ground-state preparation and use Hadamard-test protocols to probe nonclassical phonon statistics. For the Yukawa-SYK model, they show how random Majorana-boson couplings can be compiled into Rabi-gate blocks to study signatures of quantum chaos. The framework is designed to be compatible with near-term superconducting quantum hardware, avoiding the need for costly bosonic qubit encodings.

Simulating strongly correlated fermion-phonon systems is essential for understanding phenomena like polaron formation, charge-density waves, and high-temperature superconductivity. By leveraging the natural bosonic Hilbert space of microwave resonators, this approach significantly reduces the qubit count required for many-body simulations. This makes it feasible to investigate complex quantum phases and chaotic dynamics on current superconducting platforms, providing a scalable path toward studying materials where electron-phonon interactions play a dominant role.