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arXiv:2502.19156

Digital-Analog quantum Rabi simulation in the Deep Strong Coupling Regime

Noureddine Rochdi, R. Ahl Laamara, Mohamed Bennai

Published Feb 26, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the quantum Rabi model (QRM) in the deep strong coupling (DSC) regime. To capture the full dynamics of the QRM in the DSC regime, we implemented single-qubit rotations combined with integrated digital steps and qubit-bosonic blocks. This approach leads to a paradigm known as digital analog quantum simulations (DAQSs). In this work, we review the encoding of QRM in the DSC regime through emerging paradigms of digital and analog techniques. Using DAQSs encoding, an efficient simulation can be performed on state-of-the-art circuit quantum electrodynamics platforms. Finally, we provide detailed information on the dynamics of the QRM in varity of parameter regions. We demonstrate the effectiveness of the DAQS paradigms in achieving prolonged coherent measurements during time evolution, even in the case of perturbative DSC regime dynamics. This proposal lays the groundwork for simulating complex many-body dynamics that involve bosonic modes.

DOI
10.48550/arxiv.2502.19156

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We study the quantum Rabi model (QRM) in the deep strong coupling (DSC) regime. To capture the full dynamics of the QRM in the DSC regime, we implemented single-qubit rotations combined with integrated digital steps and qubit-bosonic blocks. This approach leads to a paradigm known as digital analog quantum simulations (DAQSs). In this work, we review the encoding of QRM in the DSC regime through emerging paradigms of digital and analog techniques. Using DAQSs encoding, an efficient simulation can be performed on state-of-the-art circuit quantum electrodynamics platforms. Finally, we provide detailed information on the dynamics of the QRM in varity of parameter regions. We demonstrate the effectiveness of the DAQS paradigms in achieving prolonged coherent measurements during time evolution, even in the case of perturbative DSC regime dynamics. This proposal lays the groundwork for simulating complex many-body dynamics that involve bosonic modes.
The Quantum Rabi model is a crucial theoretical framework for understanding the interplay between light and matter. This paper focuses on a transformative digital quantum simulation that utilizes Trotterization with an increased number of steps to analyze a complex unitary Hamiltonian. This method demonstrates the advantages of digital techniques in capturing the dynamic behaviors of Quantum Rabi models in the deep strong coupling regime. Moreover, this proposal highlights the universality, flexibility, and scalability of digital methods, particularly in coherent measurements during time evolution with varying photon counts.
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
The quantum Rabi model describing the fundamental interaction between light and matter is a cornerstone of quantum physics. It predicts exotic phenomena like quantum phase transitions and ground-state entanglement in ultrastrong and deep-strong coupling regimes, where coupling strengths are comparable to or larger than subsystem energies. Demonstrating dynamics remains an outstanding challenge, the few experiments reaching these regimes being limited to spectroscopy. Here, we employ a circuit quantum electrodynamics chip with moderate coupling between a resonator and transmon qubit to realise accurate digital quantum simulation of deep-strong coupling dynamics. We advance the state of the art in solid-state digital quantum simulation by using up to 90 second-order Trotter steps and probing both subsystems in a combined Hilbert space dimension of ∼80, demonstrating characteristic Schrödinger-cat-like entanglement and large photon build-up. Our approach will enable exploration of extreme coupling regimes and quantum phase transitions, and demonstrates a clear first step towards larger complexities such as in the Dicke model.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.
The Quantum Rabi model serves as a pivotal theoretical framework for elucidating the nuanced interplay between light and matter. Utilizing circuit quantum electrodynamics on a chip, we address the challenge of achieving deep strong coupling in Quantum Cavity Electrodynamics (cQED). Despite progress in superconducting circuits and trapped ions, experimental realization has been limited to spectroscopy. Our focus is on a transformative digital quantum simulation, employing Trotterization with an augmented number of steps to deconstruct a complex unitary Hamiltonian. This approach showcases the benefits of digital techniques within superconducting circuits, offering universality, flexibility, scalability, and high fidelity. Our goal is to demonstrate deep strong coupling in cQED and understand the advantages of digital methods, particularly in coherent measurement during time evolution with varying photon counts in resonators. This opens avenues to leverage quantum mechanics for overcoming hardware limitations.