Quantum Feedback Research Articles

Continuous Coherent Quantum Feedback with Time Delays: Tensor Network Solution

In this paper, we develop a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent Markovian driven dissipative quantum many-body problems. In this work, we show that the resulting Markovian quantum many-body problems can be solved (numerically) exactly and efficiently using tensor network methods for a series of paradigmatic examples, consisting of driven quantum systems coupled to waveguides at several distant points. In particular, we show that our method allows solving problems in so far inaccessible regimes, including problems with arbitrary long time delays and arbitrary numbers of excitations in the delay lines. We obtain solutions for the full real-time dynamics as well as the steady state in all these regimes. Finally, motivated by our results, we develop a novel mean-field approach, which allows us to find the solution semianalytically, and we identify parameter regimes where this approximation is in excellent agreement with our tensor network results. Published by the American Physical Society 2024

Fundamental Limits of Feedback Cooling Ultracold Atomic Gases.

We investigate the fundamental viability of cooling ultracold atomic gases with quantum feedback control. Our Letter shows that the trade-off between the resolution and destructiveness of optical imaging techniques imposes constraints on the efficacy of feedback cooling, and that rapid rethermalization is necessary for cooling thermal gases. We construct a simple model to determine the limits to feedback cooling set by the visibility of density fluctuations, measurement-induced heating, and three-body atomic recombination. We demonstrate that feedback control can rapidly cool high-temperature thermal clouds in quasi-2D geometries to degenerate temperatures with minimal atom loss compared to traditional evaporation. Our analysis confirms the feasibility of feedback cooling ultracold atomic gases, providing a pathway to new regimes of cooling not achievable with current approaches.

Federated quantum long short-term memory (FedQLSTM)

Quantum federated learning (QFL) can facilitate collaborative learning across multiple clients using quantum machine learning (QML) models, while preserving data privacy. Although recent advances in QFL span different tasks like classification while leveraging several data types, no prior work has focused on developing a QFL framework that utilizes temporal data to approximate functions useful to analyze the performance of distributed quantum sensing networks. In this paper, a novel QFL framework that is the first to integrate quantum long short-term memory (QLSTM) models with temporal data is proposed. The proposed federated QLSTM (FedQLSTM) framework is exploited for performing the task of function approximation. In this regard, three key use cases are presented: Bessel function approximation, sinusoidal delayed quantum feedback control function approximation, and Struve function approximation. Simulation results confirm that, for all considered use cases, the proposed FedQLSTM framework achieves a faster convergence rate under one local training epoch, minimizing the overall computations, and saving 25–33% of the number of communication rounds needed until convergence compared to an FL framework with classical LSTM models.

Improving robustness of quantum feedback control with reinforcement learning

Improving robustness of quantum feedback control with reinforcement learning

Quantum Measurement and Feedback Control in Quantum Systems

Quantum Measurement and Feedback Control in Quantum Systems

Protecting the Quantum Coherence of Two Atoms Inside an Optical Cavity by Quantum Feedback Control Combined with Noise-Assisted Preparation

We propose a theoretical scheme to enhance quantum coherence and obtain steady-state coherence by combining quantum feedback control and noise-assisted preparation. We investigate the effects of quantum-jump-based feedback control and noise field on the quantum coherence and excited-state population between two atoms inside an optical cavity where a noise field drives one, and the other is under quantum feedback control. It is found that steady quantum coherence can be achieved by adding an external noise field, and the quantum feedback can prolong the coherence time with partial suppression of the spontaneous emission of atoms. In addition, we study the influence of the joint action of quantum feedback and noise-assisted preparation on quantum coherence and show that the combined action of feedback control and noise-assisted preparation is more effective in enhancing steady coherence. The findings of our research offer some general guidelines for improving the steady-state coherence of coupled qubit systems and have the potential to be applied in the realm of quantum information technology.

Quantum physics cannot be captured by classical linear hidden variable theories even in the absence of entanglement

Recent experimental tests of Bell inequalities confirm that entangled quantum systems cannot be described by local classical theories but still do not answer the question whether or not quantum systems could, in principle, be modeled by linear hidden variable theories. In this paper, we study the quantum trajectories of a single qubit that experiences a sequence of repeated generalized measurements. It is shown that this system, which constitutes a hidden quantum Markov model, is more likely to produce complex time correlations than any classical hidden Markov model with two output symbols. From this, we conclude that quantum physics cannot be replaced by linear hidden variable theories. Indeed, it has already been recognized that not only entanglement but also non-classical time correlations of quantum systems with quantum feedback are a valuable resource for quantum technology applications.

Enhancing quantum discord in v-shaped plasmonic waveguides by quantum feedback

We investigate the impact of a symmetric quantum feedback control on the quantum discord of the X state in V-shaped plasmonic waveguides. Under this feedback, the quantum discord of the Werner state is enhanced from 0 to 0.38. This value even continues to rise after reducing the decay rate of the atoms. Furthermore, we get the operational mechanism of feedback control through the evolution of the matrix elements. It confines the initial 4 × 4 matrix into a 3 × 3 subspace. As a result, the weights of each ground state in the quantum state change, which suppresses the degradation of Bell state. Lastly, we propose a direction for suggesting an improved feedback Hamiltonian.

No-Collapse Accurate Quantum Feedback Control via Conditional State Tomography

No-Collapse Accurate Quantum Feedback Control via Conditional State Tomography

Realizing a deep reinforcement learning agent for real-time quantum feedback

Realizing the full potential of quantum technologies requires precise real-time control on time scales much shorter than the coherence time. Model-free reinforcement learning promises to discover efficient feedback strategies from scratch without relying on a description of the quantum system. However, developing and training a reinforcement learning agent able to operate in real-time using feedback has been an open challenge. Here, we have implemented such an agent for a single qubit as a sub-microsecond-latency neural network on a field-programmable gate array (FPGA). We demonstrate its use to efficiently initialize a superconducting qubit and train the agent based solely on measurements. Our work is a first step towards adoption of reinforcement learning for the control of quantum devices and more generally any physical device requiring low-latency feedback.

Control Landscape of Measurement-Assisted Transition Probability for a Three-Level Quantum System with Dynamical Symmetry

Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is 1/2, whereas it is about 0.687 using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.

Optimal and Variational Multiparameter Quantum Metrology and Vector-Field Sensing

We study multi-parameter sensing of 2D and 3D vector fields within the Bayesian framework for $SU(2)$ quantum interferometry. We establish a method to determine the optimal quantum sensor, which establishes the fundamental limit on the precision of simultaneously estimating multiple parameters with an $N$-atom sensor. Keeping current experimental platforms in mind, we present sensors that have limited entanglement capabilities, and yet, significantly outperform sensors that operate without entanglement and approach the optimal quantum sensor in terms of performance. Furthermore, we show how these sensors can be implemented on current programmable quantum sensors with variational quantum circuits by minimizing a metrological cost function. The resulting circuits prepare tailored entangled states and perform measurements in an appropriate entangled basis to realize the best possible quantum sensor given the native entangling resources available on a given sensor platform. Notable examples include a 2D and 3D quantum ``compass'' and a 2D sensor that provides a scalable improvement over unentangled sensors. Our results on optimal and variational multi-parameter quantum metrology are useful for advancing precision measurements in fundamental science and ensuring the stability of quantum computers, which can be achieved through the incorporation of optimal quantum sensors in a quantum feedback loop.

Quantum feedback induced genuine magnon–photon–magnon entanglement and steering in a cavity magnonical system

We present an alternative scheme to generate genuine tripartite entanglement and steering among one photon and two magnons in a cavity magnonical system, where two yttrium iron garnet spheres are respectively placed inside two microwave cavities driven by a two-mode squeezed field and subjected to homodyne-measurement feedback. It is found that quantum feedback on two cavities plays a crucial role in enhancing quantum correlations of photons and magnons. In the absence of measurement feedback, only bipartite entanglement between two magnons is existent. In contrast, when the continuous measurement feedback is present, two magnons are strongly entangled and magnon–photon entanglement also appears. More importantly, the stable genuine magnon–photon–magnon tripartite entanglement and steering could be obtained based on the homodyne-measurement feedback on two microwave cavities, which are robust against the thermal fluctuations. The work we present provides a feasible way to manipulate the multipartite quantum correlations including entanglement and steering in hybrid quantum systems.

Quantum Feedback at the Solid-Liquid Interface: Flow-Induced Electronic Current and Its Negative Contribution to Friction

A new quantum-mechanical theory predicts that a neutral liquid can generate an electric current in the solid wall along which it flows. The current in turn reduces the friction at the liquid-solid interface.

Measurement-Based Quantum Thermal Machines with Feedback Control

We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Quantum jump metrology in a two-cavity network

Quantum metrology enhances measurement precision by utilising the properties of quantum physics. In interferometry, this is typically achieved by evolving highly-entangled quantum states before performing single-shot measurements to reveal information about an unknown parameter. While this is often the optimum approach, implementation with all but the smallest states is still extremely challenging. An alternative approach is quantum jump metrology [L. A. Clark et al., Phys. Rev. A 99, 022102 (2019)] which deduces information by continuously monitoring an open quantum system, while inducing phase-dependent temporal correlations with the help of quantum feedback. Taking this approach here, we analyse measurements of a relative phase in an optical network of two cavities with quantum feedback in the form of laser pulses. It is shown that the proposed approach can exceed the standard quantum limit without the need for complex quantum states while being scalable and more practical than previous related schemes.

State initialization of a hot spin qubit in a double quantum dot by measurement-based quantum feedback control

A measurement-based quantum feedback protocol is developed for spin-state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting cavity. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be preset. Being able to preset the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts toward scaling up the number of qubits in quantum computers.

Quantum Feedback Control Outside of the Controlled System

Quantum Feedback Control Outside of the Controlled System

Quantum feedback control in quantum photosynthesis

A model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons is introduced. Quantum feedback in this approach describes the Landau--Zener transition with decoherence. The model explains irreversibility in the process of charge separation for quantum photosynthesis -- direct transitions for this quantum control model will have probabilities close to one and reverse transitions will have probabilities close to zero. This can be considered as a model of quantum ratchet. Also this model explains coincidence of energy of the vibron paired to the transition and Bohr frequency of the transition.

Generalized quantum assisted simulator

We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical–quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in three disjoint steps. First, we select the ansatz, followed by measuring overlap matrices on a quantum computer. The final step involves classical post-processing data from the second step. Our algorithm has potential applications in solving the Navier–Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems. Our entire framework is compatible with current experiments and can be implemented immediately.