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arXiv:2301.07254 · Physical Review Letters

No-Collapse Accurate Quantum Feedback Control via Conditional State Tomography

Sangkha Borah, Bijita Sarma

Published Nov 21, 2023• 2 citations
arXivHTMLPDF

Abstract

The effectiveness of measurement-based feedback control protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records to determine an accurate control strategy. To circumvent such limitations, this Letter explores a real-time stochastic state estimation approach that enables noise-free monitoring of the conditional dynamics including the full density matrix of the quantum system using noisy measurement records within a single quantum trajectory-a method we name as "conditional state tomography." This, in turn, enables the development of precise measurement-based feedback control strategies that lead to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise and has potential applications in various feedback quantum control scenarios. This approach is particularly useful for reinforcement-learning-(RL) based control, where the RL-agent can be trained with arbitrary conditional averages of observables, and/or the full density matrix as input (observation), to quickly and accurately learn control strategies.

DOI
10.1103/physrevlett.131.210803

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The effectiveness of measurement-based feedback control protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records to determine an accurate control strategy. To circumvent such limitations, this Letter explores a real-time stochastic state estimation approach that enables noise-free monitoring of the conditional dynamics including the full density matrix of the quantum system using noisy measurement records within a single quantum trajectory-a method we name as "conditional state tomography." This, in turn, enables the development of precise measurement-based feedback control strategies that lead to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise and has potential applications in various feedback quantum control scenarios. This approach is particularly useful for reinforcement-learning-(RL) based control, where the RL-agent can be trained with arbitrary conditional averages of observables, and/or the full density matrix as input (observation), to quickly and accurately learn control strategies.
This paper presents an adaptive quantum state collapse control algorithm designed to mitigate the detrimental effects of environmental noise on quantum states. The core of the algorithm relies on a reinforcement learning (RL) framework to dynamically adjust control strategies based on real-time feedback from the quantum environment. Specifically, a controller is constructed utilizing an RL agent that interacts with the quantum system, learning an optimal control policy to minimize state collapse. A key element is the integration of quantum decoherence techniques to reduce the impact of noise. The algorithm's adaptive nature allows it to contend with fluctuating noise levels, a significant challenge in maintaining the coherence of fragile quantum states. The proposed approach offers a novel method for controlling quantum systems, overcoming the limitations of conventional quantum control methods which often rely on static control parameters. The results demonstrate the efficacy of this dynamic control strategy in preserving quantum state fidelity under varying noise conditions. This work contributes to the development of robust quantum control protocols for applications such as quantum computation and quantum sensing.
Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.
Quantum state tomography (QST) is a fundamental technique for characterizing the state of a quantum system. However, traditional QST protocols often require a large number of measurements, leading to significant experimental overhead and uncertainties in the reconstructed state. This paper proposes a novel approach to QST that leverages reinforcement learning (RL) to dynamically adapt measurement strategies. The core idea is to train an RL agent to control the parameters of the QST experiment, learning to optimize the measurement process based on feedback from the acquired data. The agent learns to select measurement bases and angles that minimize the uncertainty in the reconstructed quantum state. This adaptive strategy significantly reduces the number of measurements needed compared to traditional QST while maintaining high accuracy. We present a theoretical framework for this approach, outlining the key components and demonstrating its potential for improved QST performance. The proposed method offers a promising direction for enhancing the efficiency and reliability of QST, contributing to the advancement of quantum information processing.
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This paper investigates the application of reinforcement learning (RL) for adaptive quantum control. Traditional quantum control methods often rely on pre-designed pulse shapes optimized for specific scenarios, lacking adaptability to variations in system parameters or environmental noise. This work proposes a novel framework where an RL agent learns to dynamically adjust quantum control pulses in real-time, maximizing the fidelity of quantum operations. The agent receives feedback from the quantum system, typically measured through state variables, and utilizes this information to optimize the control pulse sequence. This adaptive approach addresses the limitations of static control schemes and promises enhanced robustness and performance in complex quantum systems. The core claim centers on utilizing reinforcement learning to design optimal quantum control pulses. The central mechanism involves a trained controller dynamically adjusting pulses based on system feedback. The presented methodology offers a new approach to quantum control, particularly relevant in noisy environments and systems with parameter variations. The research demonstrates the potential of RL for achieving superior quantum control outcomes compared to conventional techniques. ---
Reinforcement Learning (RL) techniques have been increasingly applied in optimizing control systems. However, their application in quantum systems is hampered by the challenge of performing closed-loop control due to the difficulty in measuring these systems. This often leads to reliance on assumed models, introducing model bias, a problem that is exacerbated in open quantum dynamics where Markovian approximations are not valid. To address these challenges, we propose a novel approach that incorporates the non-Markovian nature of the environment into a low-dimensional effective reservoir. By initially employing a series of measurements as a 'dataset', we utilize machine learning techniques to learn the effective quantum dynamics more efficiently than traditional tomographic methods. Our methodology aims to demonstrates that by integrating reinforcement learning with model learning, it is possible to devise control policies and models that can counteract decoherence in a spin-boson system. This approach may not only mitigates the issues of model bias but also provides a more accurate representation of quantum dynamics, paving the way for more effective quantum control strategies.