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Efficient Counterdiabatic Driving for Fast and High-Fidelity State Preparation in Jaynes-Cummings Lattices


Core Concepts
A local counterdiabatic driving scheme is developed to enable fast and high-fidelity state preparation in Jaynes-Cummings lattices, overcoming the limitations of adiabatic evolution.
Abstract

The content presents a scheme that utilizes local counterdiabatic (CD) driving to provide fast and high-fidelity state preparation in Jaynes-Cummings (JC) lattices. JC lattices, consisting of arrays of JC models, can demonstrate rich physical phenomena but preparing desired quantum states in these systems is challenging due to the requirement for slow adiabatic evolution.

The authors first derive the exact CD Hamiltonian for JC lattices with one excitation, which contains nonlocal couplings between qubits and cavities at different and distant sites, making it difficult to implement in practice. To address this, the authors leverage the symmetries of the eigenstates under both periodic and open boundary conditions to derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian.

Numerical simulations confirm the effectiveness of the local CD driving scheme in comparison to the adiabatic evolution and the exact CD Hamiltonian. The authors also demonstrate the use of this method for the generation of multipartite W-states in qubits. The implementation and decoherence of this scheme in superconducting quantum devices are discussed, showing its potential for practical applications in quantum information processing.

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Stats
The magnitude of the local CD driving is on the same order of magnitude as the couplings g and J. The dimensionless time T = 0.5π corresponds to 2.5 ns, and T = 5π corresponds to 25 ns. A typical qubit decoherence time of 100 μs corresponds to a dimensionless decoherence rate γ = 5/π × 10−5. For a cavity frequency of ωc/2π ∼ 5 GHz and a quality factor Q = 106, the cavity decay rate is κ = 5 × 10−5 in dimensionless unit.
Quotes
"The exact CD Hamiltonian only includes nonzero matrix elements between eigenstates of the same wave vector k. This is because the variation of the adiabatic Hamiltonian only induces transitions between eigenstates of the same k due to the symmetry of the eigenstates." "Leveraging the symmetries of the eigenstates in JC lattices under both periodic and open boundary conditions, we derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian."

Key Insights Distilled From

by A. Govindara... at arxiv.org 10-01-2024

https://arxiv.org/pdf/2409.19186.pdf
Local Counterdiabatic Driving for Jaynes-Cummings Lattices

Deeper Inquiries

How can the local CD driving scheme be extended to JC lattices with higher excitations or more complex many-body states?

The local counterdiabatic (CD) driving scheme can be extended to Jaynes-Cummings (JC) lattices with higher excitations by generalizing the Hamiltonian to account for multiple excitations in the system. In the case of higher excitations, the eigenstates of the JC model become more complex, and the interactions between multiple qubits and cavity modes must be considered. This can be achieved by constructing a local CD Hamiltonian that incorporates the additional degrees of freedom associated with higher excitation levels. One approach is to leverage the symmetries of the eigenstates in the JC lattice, similar to the method used for one excitation. By analyzing the structure of the eigenstates and their corresponding energy levels, one can derive a local CD Hamiltonian that maintains the same block-diagonal form in the k-space basis. This would involve identifying the relevant coupling strengths and detuning parameters for the additional excitations and ensuring that the local CD driving effectively cancels out the unwanted diabatic transitions. Moreover, for more complex many-body states, such as entangled states or states exhibiting quantum phase transitions, the local CD driving can be adapted by incorporating additional local interactions that reflect the specific characteristics of the target state. This may involve tuning the local couplings dynamically during the evolution to match the desired state preparation protocol. Numerical simulations can be employed to validate the effectiveness of the extended local CD driving scheme in achieving high-fidelity state preparation in these more complex scenarios.

What are the potential limitations or trade-offs of the local CD driving approach compared to other state preparation techniques, such as optimal control or variational quantum algorithms?

While the local CD driving approach offers significant advantages in terms of eliminating diabatic transitions and enabling fast state preparation, it also presents certain limitations and trade-offs compared to other state preparation techniques like optimal control or variational quantum algorithms. Implementation Complexity: The local CD driving scheme requires precise control over local couplings and detuning parameters, which may be challenging to achieve in practice, especially in noisy quantum devices. In contrast, optimal control techniques can often be more flexible, allowing for the design of control pulses that can adapt to the specific characteristics of the quantum system. Scalability: As the number of qubits and excitations increases, the complexity of the local CD Hamiltonian may grow significantly, potentially leading to difficulties in implementation. Optimal control methods, on the other hand, can be more scalable as they can be designed to work with larger systems without the need for explicit derivation of the Hamiltonian. Robustness to Noise: Local CD driving may still be susceptible to decoherence effects, particularly in systems with long evolution times. While it mitigates diabatic transitions, it does not inherently address the issue of environmental noise. Variational quantum algorithms, which often incorporate error mitigation techniques, may provide better robustness against noise in practical implementations. Resource Requirements: The local CD driving approach may require additional resources in terms of control precision and timing, which could limit its practicality in certain experimental setups. In contrast, variational quantum algorithms can leverage existing quantum hardware more effectively by optimizing the parameters of a predefined circuit. In summary, while local CD driving is a powerful technique for state preparation, its practical implementation may face challenges related to complexity, scalability, noise robustness, and resource requirements compared to other state preparation methods.

Could the insights from this work on exploiting symmetries in JC lattices be applied to the development of efficient counterdiabatic driving schemes for other many-body quantum systems?

Yes, the insights gained from exploiting symmetries in Jaynes-Cummings (JC) lattices can indeed be applied to the development of efficient counterdiabatic driving schemes for other many-body quantum systems. The key principles underlying the local CD driving approach, particularly the identification and utilization of symmetries in the eigenstates, are broadly applicable across various quantum systems. Symmetry Exploitation: Many-body quantum systems often exhibit symmetries that can be leveraged to simplify the construction of counterdiabatic Hamiltonians. By analyzing the symmetry properties of the eigenstates, one can derive local CD Hamiltonians that maintain the same dynamical behavior as their non-local counterparts, similar to the approach taken in JC lattices. Generalization to Other Models: The methodology used to derive the local CD Hamiltonian in JC lattices can be generalized to other models, such as spin chains, fermionic systems, or bosonic lattices. By understanding the specific symmetries and interactions present in these systems, researchers can formulate local CD driving schemes that are experimentally feasible. Application to Quantum Simulation: The insights from this work can enhance the efficiency of quantum simulations of complex many-body phenomena. By implementing local CD driving, one can prepare desired quantum states more rapidly and with higher fidelity, facilitating the exploration of quantum phase transitions, topological states, and other emergent phenomena in various quantum systems. Interdisciplinary Impact: The principles of local CD driving and symmetry exploitation can also find applications in other fields, such as quantum chemistry and condensed matter physics, where many-body interactions play a crucial role. This could lead to advancements in state preparation techniques for simulating chemical reactions or studying exotic phases of matter. In conclusion, the insights from the local CD driving scheme in JC lattices provide a valuable framework for developing efficient counterdiabatic driving strategies in a wide range of many-body quantum systems, potentially leading to significant advancements in quantum state preparation and manipulation.
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