New Control Strategy Enhances Stability in Open Qubit Systems, Boosts Quantum State Transitions

Researchers from various universities and research centers have developed a new switching control strategy for open qubit systems based on Lyapunov control. The strategy uses coherent vector representation to prevent the qubit state from entering invariant sets and singular value sets, driving the system to a small neighborhood of target states.

This relaxes the strict constraints on system models imposed by special target states. The strategy also identifies conditions for achieving finite-time stability and finite-time contractive stability, improving quantum state transitions. The research, supported by the National Natural Science Foundation of China, could lead to advancements in quantum information technologies.

What is the New Switching Control Strategy for Open Qubit Systems?

A team of researchers from the Department of Automation at Shanghai Jiao Tong University, the Key Laboratory of System Control and Information Processing, the Shanghai Engineering Research Center of Intelligent Control and Management, the School of Automation at Central South University, the Department of Automation at the University of Science and Technology of China, and the School of Engineering at the Australian National University have developed a new switching control strategy for open qubit systems. This strategy is based on Lyapunov control, a method that uses Lyapunov stability to design control laws that stabilize a system to a target state.

The team’s strategy uses coherent vector representation to prevent the state of the qubit from entering invariant sets and singular value sets. This effectively drives the system to a sufficiently small neighborhood of target states. Compared to existing works, this control strategy relaxes the strict constraints on system models imposed by special target states.

The researchers also identified conditions under which the open qubit system achieves finite-time stability (FTS) and finite-time contractive stability (FTCS). This represents a significant improvement in quantum state transitions, especially considering the asymptotic stability of arbitrary target states is unattainable in open quantum systems.

How Does This Strategy Improve Quantum State Transitions?

The team’s switching control strategy represents a critical improvement in quantum state transitions. In open quantum systems, the asymptotic stability of arbitrary target states is unattainable. However, the researchers’ strategy can guide the state of the qubit to a small neighborhood of target states, effectively driving the system to its desired state.

The strategy also identifies conditions under which the open qubit system achieves finite-time stability (FTS) and finite-time contractive stability (FTCS). These concepts consider practical constraints and the need for a swift response, aiming to ensure that the system attains and maintains proximity to the target state within a finite time.

The effectiveness of the proposed method is convincingly demonstrated through its application in a qubit system affected by various types of decoherence, including amplitude dephasing and polarization decoherence.

What is the Significance of This Research in Quantum Information Processing?

Qubit systems, the basic carrier of quantum information, play a crucial role in quantum information processing. Precise control of qubit states is fundamental to the success of quantum communication and control and is pivotal in advancing the field of quantum information technologies.

The team’s research addresses a fundamental control problem: how to guide the state of qubit systems toward a target state via suitable controls. Their switching control strategy for open qubit systems represents a significant step forward in this area.

How Does This Strategy Compare to Existing Methods?

Existing methods for controlling open quantum systems are usually more challenging. To achieve global asymptotic stability in state transition, target states have to be chosen as special states. Most existing works focus on specific target states, and the existing control laws often do not work for arbitrary target states.

In contrast, the team’s switching control strategy does not require the target state to be the eigenstate of the system Hamiltonian or commute with Lindblad operators. It employs a switching control strategy to prevent the state from entering invariant and singular value sets. This makes it possible to guide the state of the qubit to a small neighborhood of target states, effectively driving the system to its desired state.

What are the Future Implications of This Research?

The team’s research opens up new possibilities for the control of open qubit systems. Their switching control strategy, which can guide the state of the qubit to a small neighborhood of target states, represents a significant improvement in quantum state transitions.

The strategy’s ability to achieve finite-time stability (FTS) and finite-time contractive stability (FTCS) under certain conditions also has important implications for the practical application of open qubit systems. These concepts consider practical constraints and the need for a swift response, which is crucial in many quantum information processing applications.

The research also provides a foundation for further exploration and development in this area. Future research could build on this work to develop more advanced control strategies for open qubit systems, potentially leading to significant advancements in quantum information technologies.