Researchers Shimpei Goto and Kazuki Koshino from Tokyo Medical and Dental University have developed a new method for labeling the eigenstates of qubit-cavity systems, a fundamental setup in studying quantum light-matter interaction and crucial for superconducting quantum computation. The method, based on the continuity of the qubit occupancy, provides an estimation of a quantum state’s evolution under cavity driving. It also allows for the estimation of the photon-number dependence of the resonant cavity frequency. The team also explored the offset charge dependence of resonances to higher qubit excited states in the transmon-cavity system.
Introduction to Qubit-Cavity Systems
Shimpei Goto and Kazuki Koshino from the College of Liberal Arts and Sciences at Tokyo Medical and Dental University have proposed a new method for labeling the eigenstates of qubit-cavity systems. This method is based on the continuity of the qubit occupancy and can provide a rough estimation of the evolution of a quantum state under cavity driving. The researchers suggest that the photon-number dependence of the resonant cavity frequency can be estimated from the labeled eigenenergies. Furthermore, resonances to higher excited qubit states are visible in the dependence.
The Importance of Qubit-Cavity Systems
Qubit-cavity systems are fundamental setups to study the quantum light-matter interaction. They are essential building blocks for superconducting quantum computation as the readout of the qubit state can be performed with the setup by the dispersive readout. The qubit used in the superconducting circuits has some complexities that are absent in the Jaynes-Cummings model. These complexities should be considered when studying qubit-cavity systems for practical applications.
The Proposed Labeling Method
The proposed method can be applied to a broader parameter region compared to an existing method. The researchers found instances where the existing method gives suspicious discontinuous photon-number dependence of qubit occupancy. Thus, they developed a new approach that estimates continuous dependence even in such cases. The evolution of the qubit occupancy roughly follows the photon-number dependence given by the proposed method.
Investigating the Offset Charge Dependence
Using the proposed method, the researchers also investigated the offset charge dependence of resonances to higher qubit excited states in the transmon-cavity system. They observed that the locations of the resonances strongly depend on the offset charge and that only around ten photons can induce a transition leading to leakage from the computational space.
Labeling Methods
The purpose of the paper is to propose a new method to label the eigenstates of qubit-cavity systems. The Hamiltonian of the qubit-cavity system is given by a specific formula. The researchers discuss how to find a labeled state for a qubit state and a Fock state from the eigenstates. The eigenenergy of the labeled eigenstate is denoted by a specific symbol. With the labeled eigenenergies, one can regard the difference between two eigenenergies as the effective cavity frequency when the qubit is initially in a certain state and the cavity photon number is a certain number.
The Overlap Approach
The simplest approach to find the labeled state is the overlap approach. This method does not work in a large region as presented in Section III. The failure of the overlap approach means that the labeled state cannot be represented as a certain formula for the large region.
Recursive Approach
A recursive approach proposed in a reference can be applied to nonpreserving systems. Starting from an initial state, a state is obtained from the previous state recursively. In the recursive approach, a state is used to find the next state.
The article titled “Labeling eigenstates of qubit-cavity systems based on the continuity of qubit occupancy: Detecting resonances to higher excited qubit states” was published on January 29, 2024. The authors of this article are Shimpei Goto and Kazuki Koshino. The article was published on arXiv, a platform managed by Cornell University. The article discusses the labeling of eigenstates in qubit-cavity systems and the detection of resonances to higher excited qubit states. The DOI reference for this article is https://doi.org/10.48550/arxiv.2401.16666.
Source: arXiv (Cornell University)
