The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control theory and machine learning to predict the future evolution of a qubit's state; we deploy this information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time-division multiplexed approach, interleaving measurement periods with periods of unsupervised but stabilised operation during which qubits are available, for example, in quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as encountered in passive frequency standards. Both experiments demonstrate significant improvements in qubit-phase stability over 'traditional' measurement-based feedback approaches by exploiting time domain correlations in the noise processes. This technique requires no additional hardware and is applicable to all two-level quantum systems where projective measurements are possible.
The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control theory and machine learning to predict the future evolution of a qubit's state; we deploy this information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time-division multiplexed approach, interleaving measurement periods with periods of unsupervised but stabilised operation during which qubits are available, for example, in quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as encountered in passive frequency standards. Both experiments demonstrate significant improvements in qubit-phase stability over 'traditional' measurement-based feedback approaches by exploiting time domain correlations in the noise processes. This technique requires no additional hardware and is applicable to all two-level quantum systems where projective measurements are possible.
Combating decoherence---the randomization of qubit values in a physical system---is a key challenge in quantum computing. Control theory provides a powerful set of tools to stabilize classical systems, but much work remains to bring its full weight to the quantum domain. Aiming to track and predict qubit-state evolution under various forms of decoherence, the authors employ machine-learning algorithms to optimize qubit-state forecasting, and adapt classical algorithms to work directly with discrete, single-shot qubit measurements. These results suggest that exciting opportunities exist for implementing real-time feedback using purely classical, hardware-agnostic techniques.
Quantum-enabled technologies promise advancements across a huge range of industrial, metrological and medical applications and are already demonstrating significant impacts, especially in the realm of sensing and metrology. While the extreme sensitivity of quantum systems to their environment is fueling those applications, it also represents a major hurdle to technologies which require long-term stability such as quantum computing and quantum simulations. In addition to the inherent decoherence phenomenon, the challenge associated with controlling a quantum system accurately and precisely, does in fact impede all of the aforementioned applications. Such techniques have therefore been subject to extensive research in both the academic and industrial sector and as a result, sophisticated quantum control techniques are emerging in order to understand, characterize and mitigate errors in quantum systems. This thesis presents how quantum control techniques can be employed to characterize and suppress both control imperfections and environmental noise in quantum systems, using experiments with trapped ions as a model quantum platform. We demonstrate two distinct but interrelated approaches that leverage either time-domain or frequency-domain information about the noise. In the first approach, we show how supervised learning algorithms can efficiently extract time-domain correlations from time-stamped sequences of projective measurements on a qubit. This information can then be used to perform real-time predictive control in which we autonomously pre-compensate anticipated qubit noise in order to stabilize the system. The second approach deploys provably optimal narrowband controls in order to characterize the specific spectral components of noise experienced by a qubit. Here, frequency-shifted Slepian functions permit reconstruction of system noise with maximum out-of-band rejection, and full spectrum reconstruction is enabled using techniques based on multitaper and Bayesian methods.
This paper presents a novel approach to enhancing the performance of Quantum Neural Networks (QNNs) through a dynamic decoherence suppression mechanism. Traditional decoherence mitigation strategies are often static and fail to adapt to the inherent fluctuations and noise present in quantum systems. We propose a feedback-based system that continuously monitors and corrects decoherence within the QNN, leveraging quantum measurement and control. The core claim of this work is to design a quantum feedback-based dynamic decoherence suppression mechanism to real-time monitor and correct decoherence in QNNs, thereby improving the network's computational capabilities and stability. The proposed mechanism relies on the core mechanism of utilizing quantum measurement and control to monitor and compensate for the decoherence effects, maintaining coherence between qubits. This dynamic approach addresses the limitations of static methods, offering a more robust and adaptable solution for QNNs. Mathematical formulations detailing the system dynamics and control strategies are presented, alongside a discussion of the theoretical underpinnings and potential applications. The effectiveness of the proposed mechanism is conceptually outlined, highlighting its ability to significantly improve the resilience of QNNs against environmental noise and ultimately boosting their computational performance. ---
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.
Abstract The no-knowledge quantum feedback, introduced in Phys. Rev. Lett., 113, 020407 (2014), is a measurement-based feedback protocol for decoherence suppression in a quantum system coupled to noisy environment. By continuously measuring the environmental noise, without directly gathering any information about the system, the decoherence effect can be suppressed by feeding back quantum controls proportional to the measured signal. In the original work, the feedback control was assumed instantaneous, leading to perfect cancellation of noise backaction on the quantum system. However, the instantaneous feedback is difficult to achieve in practice, and close-loop feedback protocols are always associated with finite delayed time. Therefore, in this work, we consider the effects of the delay between the time at which the measurement signal is acquired and the time that such signal is fed back to the system. We investigate the problem with an example of a two-level system (qubit) coupled to a Markovian reservoir, via a Hermitian coupling operator, where a homodyne detection is used to measure the environmental noise. We numerically simulate quantum stochastic trajectories of the qubit and analyse their averaged dynamics. We find that the feedback control with time delay can either enhance or reduce the decoherence effects, depending on whether the delayed time is in-phase or out-of-phase with the unitary dynamics of the qubit system.
This paper explores a novel approach to Bayesian inference within quantum systems, specifically addressing the significant challenge posed by decoherence. Traditional Bayesian inference relies on maintaining quantum coherence, which is highly susceptible to environmental noise. We introduce a framework where decoherence is actively mitigated through dynamically controlled environmental interactions. The core concept involves utilizing precisely engineered external fields, coupled with real-time feedback loops, to counteract decoherence effects during the inference process. Unlike passive isolation or conventional error correction strategies, our method offers an active, responsive solution that maintains coherence for extended periods. We detail the theoretical underpinnings of this approach, focusing on the mathematical formulation of the inference process, incorporating decoherence models and the control strategies employed. The proposed system leverages quantum measurement to update Bayesian probabilities, with the control parameters designed to minimize the impact of decoherence on the measurement outcomes. This work lays the groundwork for performing accurate Bayesian inference on quantum systems, potentially unlocking new possibilities in quantum computing and information processing. The key mathematical concepts employed include the Schrödinger equation, density matrix formalism, and Bayesian probability theory. The system is designed to achieve a target accuracy in the Bayesian inference, even in the presence of significant decoherence.