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Chinese Control Conference (CCC)

Control Hamiltonian selection for quantum state stabilization using deep reinforcement learning

Chunxiang Song, Yanan Liu, Daoyi Dong, Huadong Mo

Published Jul 28, 2024• 0 citations
Publisher

Abstract

Quantum state stabilization is a pivotal element in the realm of quantum control, forming the bedrock for various quantum tasks. To achieve the stabilization of a quantum state, it is imperative to formulate effective control channels (represented by control Hamiltonians) and devise the appropriate control signals. In this study, we introduce a novel approach, the selection of control Hamiltonians through Deep reinforcement learning (SCH-DRL), to address the challenge of control Hamiltonian selection in quantum control. Deep reinforcement learning (DRL) is employed to generate control signals corresponding to control Hamiltonians, and SCH-DRL utilizes these control signals to recognize a set of simple and efficient control Hamiltonians, depending on different target states. This approach not only provides a method for control Hamiltonian selection in quantum state stabilization but also unveils the untapped potential of DRL for a broad spectrum of applications in the field of quantum information. Through applications in two-qubit and three-qubit scenarios, we demonstrate how the SCH-DRL method adeptly selects the quantity of control Hamiltonians for achieving the desired stability of quantum states.

DOI
10.23919/ccc63176.2024.10662695

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Quantum state stabilization is a pivotal element in the realm of quantum control, forming the bedrock for various quantum tasks. To achieve the stabilization of a quantum state, it is imperative to formulate effective control channels (represented by control Hamiltonians) and devise the appropriate control signals. In this study, we introduce a novel approach, the selection of control Hamiltonians through Deep reinforcement learning (SCH-DRL), to address the challenge of control Hamiltonian selection in quantum control. Deep reinforcement learning (DRL) is employed to generate control signals corresponding to control Hamiltonians, and SCH-DRL utilizes these control signals to recognize a set of simple and efficient control Hamiltonians, depending on different target states. This approach not only provides a method for control Hamiltonian selection in quantum state stabilization but also unveils the untapped potential of DRL for a broad spectrum of applications in the field of quantum information. Through applications in two-qubit and three-qubit scenarios, we demonstrate how the SCH-DRL method adeptly selects the quantity of control Hamiltonians for achieving the desired stability of quantum states.
The stabilization of quantum states is a fundamental problem for realizing various quantum technologies. Measurement-based-feedback strategies have demonstrated powerful performance, and the construction of quantum control signals using measurement information has attracted great interest. However, the interaction between quantum systems and the environment is inevitable, especially when measurements are introduced, which leads to decoherence. To mitigate decoherence, it is desirable to stabilize quantum systems faster, thereby reducing the time of interaction with the environment. In this paper, we utilize information obtained from measurement and apply deep reinforcement learning (DRL) algorithms, without explicitly constructing specific complex measurement-control mappings, to rapidly drive random initial quantum state to the target state. The proposed DRL algorithm has the ability to speed up the convergence to a target state, which shortens the interaction between quantum systems and their environments to protect coherence. Simulations are performed on two-qubit and three-qubit systems, and the results show that our algorithm can successfully stabilize random initial quantum system to the target entangled state, with a convergence time faster than traditional methods such as Lyapunov feedback control and several DRL algorithms with different reward functions. Moreover, it exhibits robustness against imperfect measurements and delays in system evolution.
The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yield a final state with high-fidelity (>0.999>0.999>0.999) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful new framework for preparing and manipulating quantum critical states.
Deep reinforcement learning (DRL) has gained increasing attention in quantum physics, especially for quantum control problems, as it effectively handles high dimensionality and complex dynamics. However, many existing DRL-based quantum control methods assume full observability of quantum states, which tends to be impractical due to the massive state copies required for precise quantum measurements. To address this, we model quantum control under partial observations and introduce a memory-based DRL (MDRL) method that efficiently handles such scenarios. The proposed MDRL comprises two key components: a memory-based exploration strategy and a memory-based reward scheme. Specifically, the agent is equipped with a biology-inspired brain to memorize information derived from partial observations, including whether an episode is successful and the number of steps spent on a successful episode. The exploration strategy leverages the memorized information to guide interactions with the quantum system, while the reward scheme assigns appropriate rewards, together enabling the agent to learn an effective control strategy. The effectiveness of MDRL is verified by three examples, i.e., one-qubit state control, two-qubit state control, andTxT_{x}Tx​gate design. Numerical results demonstrate that MDRL outperforms several representative DRL algorithms for quantum control.
Abstract The preparation of quantum states is essential in the realm of quantum information processing, and the development of efficient methodologies can significantly alleviate the strain on quantum resources. Under the framework of deep reinforcement learning (DRL), we integrate the initial and the target state information within the state preparation task together, so as to realize the control trajectory design between two arbitrary quantum states. Taking a semiconductor double quantum dots (DQDs) model as an example, our results demonstrate that the resulting control trajectories can effectively achieve arbitrary quantum state preparation (AQSP) for both single-qubit and two-qubit systems, with average fidelities of 0.9868 and 0.9556 for the test sets, respectively. For the DQDs, charge and nuclear noises will exist, thus decreases the average fidelity of AQSP. We have also incorporated noise amplitude as an input feature in the training process, leading to the development of noise-aware models. The control trajectories designed by these models can effectively suppress the influence of noise. Our research validates the effectiveness of DRL in quantum state preparation and offers solutions for multi-initial and multi-objective quantum control tasks, with potential for broader application in quantum control problems.
Deep reinforcement learning (DRL) has been recognized as a powerful tool in quantum physics, where DRL's reward design is nontrivial but crucial for quantum control tasks. To address the problem of over-reliance on human empirical knowledge to design DRL's rewards, we propose a DRL with a novel reward paradigm designed by the learning process information (DRL-LPI), where the learning process information (LPI) comprises the state information and the experiences. In DRL-LPI, the state information after being classified by a fidelity threshold, and the experiences are first stored simultaneously in the respective sequences, and this process is repeated until a similar-segment ends. Then, the stored state information is converted to the real value and used to design the reward value by applying a self-amplitude function. Next, the designed reward values are integrated with the stored experiences to compose transitions for DRL's training. Through comparisons to five representative reward schemes, the proposed DRL-LPI is evaluated on two typical quantum control tasks, i.e., the spin-(1/2) quantum state control and many-coupled qubits state control, and the experimental results show the superior learning efficiency and control performance of the proposed approach. More results show that DRL-LPI exhibits the ability to learn the control strategy with few control actions compared to stochastic gradient descent (SGD) and genetic algorithm (GA).
The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yields a final state with high fidelity ( > 0.999 ) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful framework for preparing and manipulating quantum critical states.