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arXiv:2409.19186

Local Counterdiabatic Driving for Jaynes-Cummings Lattices

A. Govindarajan, Lin Tian

Published Sep 27, 2024• 0 citations
arXivHTMLPDF

Abstract

Jaynes-Cummings (JC) lattices can be constructed by connecting quantum two-level systems with cavities and have been widely studied for polariton many-body states and multipartite entanglement. Although adiabatic evolution has been studied for the generation of many-body states in this system, its reliance on long timescales can lead to serious decoherence. Here we present a scheme that utilizes local counterdiabatic (CD) driving to provide fast and high-fidelity state preparation in JC lattices. The exact CD Hamiltonian for this system contains nonlocal couplings between qubits and cavities at different and distant sites, which causes a challenge in the implementation. Leveraging the symmetries of the eigenstates under both periodic and open boundary conditions, we derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian and our numerical simulations confirm this result. We also show that a multipartite W-state can be prepared with high fidelity using this method. The implementation and decoherence of this scheme with superconducting quantum devices are also discussed.

DOI
10.48550/arxiv.2409.19186

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Jaynes-Cummings (JC) lattices can be constructed by connecting quantum two-level systems with cavities and have been widely studied for polariton many-body states and multipartite entanglement. Although adiabatic evolution has been studied for the generation of many-body states in this system, its reliance on long timescales can lead to serious decoherence. Here we present a scheme that utilizes local counterdiabatic (CD) driving to provide fast and high-fidelity state preparation in JC lattices. The exact CD Hamiltonian for this system contains nonlocal couplings between qubits and cavities at different and distant sites, which causes a challenge in the implementation. Leveraging the symmetries of the eigenstates under both periodic and open boundary conditions, we derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian and our numerical simulations confirm this result. We also show that a multipartite W-state can be prepared with high fidelity using this method. The implementation and decoherence of this scheme with superconducting quantum devices are also discussed.
In noisy quantum systems, achieving high-fidelity state preparation using the adiabatic approach faces a dilemma: either extending the evolution time to reduce diabatic transitions or shortening it to mitigate decoherence effects. Here we present a quantum shortcut to adiabaticity for state preparation in a finite-sized Jaynes-Cummings lattice by applying counterdiabatic (CD) driving along given adiabatic trajectories. Leveraging the symmetry of eigenstates in our system, we convert the CD driving to an implementable Hamiltonian that only involves local qubit-cavity couplings for a two-site lattice with one polariton excitation. Additionally, we derive a partial analytical form of the CD driving for the lattice with two excitations. Our numerical results demonstrate that circuit errors and environmental noise have negligible effects on our scheme under practical parameters. We also show that our scheme can be characterized through the detection of qubit operators. This approach can lead to a promising pathway to high-fidelity state preparation in a significantly reduced timescale when compared to conventional adiabatic methods.
Abstract One of the key questions in quantum information is the preparation of desired multipartite quantum states with high fidelity. Adiabatic evolution has been widely explored to achieve state preparation in quantum many-body systems. However, in noisy quantum systems, the adiabatic approach faces a dilemma: either extending the evolution timescales to reduce diabatic transitions or shortening the timescales to mitigate decoherence effects. Various quantum control approaches have been studied to resolve this dilemma. In a few recent works, we utilized Jaynes-Cummings (JC) lattices as a platform to investigate the potential of several quantum control techniques in preparing quantum many-body states, including the optimized adiabatic evolution approach, the quantum optimal control technique, and quantum shortcuts to adiabaticity. Here we first give an overview of our previous results on utilizing quantum optimal control in JC lattices with unit filling and utilizing local counterdiabatic driving in JC lattices with a single excitation. Then we present our results on the energy costs and energy fluctuations in these approaches. Our studies give insights into the implementation of different approaches in practical quantum devices and the connection between the energy costs and the quantum speed limit in preparing desired quantum many-body states for quantum simulation and quantum computation.
Recently, the technique of counterdiabatic driving, which provides an effective strategy for accelerating adiabatic quantum evolution, has been widely applied in the preparation of many-body quantum states. In this work, we propose a theoretical scheme for the efficient preparation of Dicke states in a system of non-interacting two-level atoms. Our approach leverages the one-axis twisting (OAT) interaction to generate non-classical correlations and combines it with time-dependent external fields to achieve precise control over the dynamics of the system. By employing rapid adiabatic passage (RAP), it demonstrates how the system can be steered from an initial coherent spin state to a target Dicke state with high fidelity [S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuletić, W. P. Schleich, and V. S. Malinovsky, Phys. Rev. Lett. \textbf{132}, 153603 (2024)]. To further optimize the preparation process, we introduce counterdiabatic driving (CD), which suppresses non-adiabatic transitions. Numerical simulations confirm that our scheme can achieve high-fidelity Dicke states for a moderate number of particles. Our results provide a scalable and experimentally feasible approach to prepare Dicke states, with potential applications in quantum metrology, quantum communication, and quantum information processing.
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
Abstract Counterdiabatic driving can suppress diabatic losses during adiabatic ground state preparation. As its implementation necessitates the generation of an adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local controls in many-body systems, local counterdiabatic driving with approximate adiabatic gauge potential has been widely adopted. In this work, using transverse-field Ising model as an example, we present an in-depth study of the performance of local counterdiabatic protocols and provide a closed-form analysis of ground-state-fidelity optimization. We then propose a two-stage protocol based on local counterdiabatic and simple local single-body control to further improve the performance. The practical implementation of these protocols does not require diagonalization of instantaneous Hamiltonians or spectral gaps, and only additional local single-body driving is involved. To benchmark their performance, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.
Abstract Strongly correlated polaritons in Jaynes–Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and superfluid phases at integer fillings. The prerequisite to observe such phase transitions is to pump polariton excitations into a JC lattice and prepare them into appropriate ground states. Despite previous efforts, it is still challenging to generate many-body states with high accuracy. Here, we present an approach for the robust preparation of many-body ground states of polaritons in finite-sized JC lattices by optimized nonlinear ramping. We apply a Landau–Zener type of estimation to this finite-sized system and derive the optimal ramping index for selected ramping trajectories, which can greatly improve the fidelity of the prepared states. With numerical simulation, we show that by choosing an appropriate ramping trajectory, the fidelity in this approach can remain close to unity in almost the entire parameter space. This approach can shed light on high-fidelity state preparation in quantum simulators and advance the implementation of quantum simulation with practical devices.