Noise-canceling quantum feedback: Non-Hermitian dynamics with applications to state preparation and magic state distillation

The uncertainty principle, a cornerstone of quantum mechanics, has evolved from a fundamental limitation into a manageable resource in quantum information science. Precise control over quantum uncertainty is crucial for ensuring the security of quantum cryptography and the advantage of quantum computation. This work investigates the control of the quantum-memory-assisted entropic uncertainty relation in a noisy two-particle qutrit system, using quantum feedback control as a suppression strategy. In our model, Bob prepares a system <i>AB</i> composed of two V-type three-level atoms and sends atom <i>A</i> to Alice. Atom <i>A</i> interacts with a bimodal dissipative cavity. To suppress decoherence, a photodetector is used to monitor the dissipative cavity. Once a photon is detected, a local quantum feedback control is applied to atom <i>A</i>. Meanwhile, Bob’s atom <i>B</i> is assumed to be isolated from the noisy environment. To quantify the uncertainty, we select two incompatible observables, <i>S<sub>x</sub></i> and <i>S<sub>z</sub></i>, corresponding to the spin-1 components. We analyze the evolution of the entropic uncertainty and its lower bound, with the system initialized in two distinct states: an excited state and a maximally entangled state. Our findings demonstrate that applying appropriate quantum feedback control to the system can significantly suppress decoherence, leading to a marked reduction in both the entropic uncertainty and its lower bound. Through numerical simulations, we identify the optimal feedback strength for minimizing the entropic uncertainty and its lower bound to be p=2 for both initial states. Furthermore, examination of the system’s steady-state behavior after prolonged evolution reveals a key insight: under optimal feedback, the initial maximally entangled state evolves into a state with maximal classical correlation. Although no quantum correlation exists in this steady state, the strong classical correlation provides Bob with partial information about atom <i>A</i>, thereby enhancing his prediction accuracy for the measurement outcomes and leading to the observed reduction in the entropic uncertainty. Additionally, we explore the dynamics of the system’s purity. The results show a clear negative correlation, indicating that the reduction in entropic uncertainty is directly attributable to the purification of the system effected by the feedback control. In conclusion, this study establishes quantum feedback control as an effective theoretical protocol for suppressing the entropic uncertainty in realistic noisy environments. It provides a viable pathway for manipulating quantum uncertainty to enhance the robustness and performance of quantum information processing tasks.

Quantum feedback control with a transformer neural network architecture

Abstract We theoretically investigate measurement-based feedback control over the motional degrees of freedom of an oblate quasi-2D atomic Bose–Einstein condensate (BEC) subject to continuous density monitoring. We develop a linear-quadratic-Gaussian model that describes the multi-mode dynamics of the condensate’s collective excitations under continuous measurement and control. Crucially, the multi-mode cold-damping feedback control we consider uses a realistic state-estimation scheme that does not rely upon a particular model of the atomic dynamics. We present analytical results showing that collective excitations can be cooled to below single-phonon average occupation (ground-state cooling) across a broad parameter regime, and identify the conditions under which the lowest steady-state phonon occupation is asymptotically achieved. Further, we develop multi-objective optimization methods that explore the trade-off between cooling speed and the final energy of the cloud, and provide numerical simulations demonstrating the ground-state cooling of the lowest ten motional modes above the condensate ground state. Our investigation provides concrete guidance on the feedback control design and parameters needed to experimentally realize a feedback-cooled BEC.

Abstract The use of quantum stochastic models is widespread in dynamical reduction, simulation of open systems, feedback control and adaptive estimation. In many applications only part of the information contained in the filter’s state is actually needed to reconstruct the target observable quantities; thus, filters of smaller dimensions could be in principle implemented to perform the same task. In this work, we propose a systematic method to find, when possible, reduced-order quantum filters that are capable of exactly reproducing the evolution of expectation values of interest. In contrast with existing reduction techniques, the reduced model we obtain is exact and in the form of a Belavkin filtering equation, ensuring physical interpretability. This is attained by leveraging tools from the theory of both minimal realization and non-commutative conditional expectations. The proposed procedure is tested on prototypical examples, laying the groundwork for applications in quantum trajectory simulation and quantum feedback control.

Abstract Entangled microwave fields are a crucial resource for quantum information processing and quantum computation. Here a scheme is presented to enhance quantum entanglement between two microwave cavity modes using coherent quantum feedback in cavity magnonics. The system consists of a planar cross‐line cavity that includes two microwave cavity modes, with a ferrimagnetic yttrium‐iron‐garnet (YIG) sphere positioned at the intersection of these modes. The magnon mode confined in the YIG sphere can simultaneously be coupled to both microwave cavity modes via magnetic dipole interaction. Additionally, a coherent feedback loop is integrated into one of the cavity modes to modulate its frequency detuning and dissipation. These results demonstrate that feedback control can effectively reduce the dissipation and effective environmental temperature, thereby relaxing the stringent requirement of quantum state generation on extremely low bath temperatures. Furthermore, by enhancing the feedback signal to reduce the high power requirement for activating magnon Kerr effect, the feasibility of the experiment is significantly improved. The scheme finds broad applications in many quantum tasks that require microwave entanglement and other research field that needs to cool quantum systems.

Quantum energy teleportation (QET) is a quantum feedback protocol in which local measurements, classical communication, and preexisting entanglement enable the extraction of energy at a distant site, without transporting physical energy carriers. Originally conceived as a theoretical manifestation of Maxwell’s demon, QET has developed into a versatile tool for probing quantum correlations, diagnosing phase transitions, and powering emergent quantum thermodynamic technologies. This brief review provides a pedagogical introduction to the theoretical foundations and recent developments of QET, including quantum operations, entropic and fidelity-based bounds, and resource analyses involving quantum discord. Additionally, recent experimental realizations on superconducting quantum computers are revisited.

Abstract Achieving unit fidelity in quantum state preparation is often impossible in the presence of environmental decoherence. While continuous monitoring and feedback control can improve fidelity, perfect state preparation remains elusive in many scenarios. Inspired by quantum speed limits, we derive a fundamental bound on the steady-state average fidelity achievable via continuous monitoring and feedback control. This bound depends only on the unconditional Lindblad dynamics, the Hamiltonian variance, and the target state. We also adapt the bound to the case of Markovian feedback strategies. We then focus on preparing Dicke states in an atomic ensemble subject to collective damping and dispersive coupling. By imposing additional constraints on control Hamiltonians and monitoring strategies, we derive tighter fidelity bounds. Finally, we propose specific control strategies and validate them using reinforcement learning. Benchmarking their performance against our theoretical bounds highlights the relevance and usefulness of these bounds in characterizing quantum feedback control strategies.

Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with a Wannier-Stark ladder

A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell demons that achieve robust feedback-controlled chiral or helical transport against noise and decoherence. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control. Published by the American Physical Society 2025

Semiclassical gravity couples classical gravity to the quantized matter in meanfield approximation. The meanfield coupling is problematic for two reasons. First, it ignores the quantum fluctuation of matter distribution. Second, it violates the linearity of the quantum dynamics. The first problem can be be mitigated by allowing stochastic fluctuations of the geometry but the second problem lies deep in quantum foundations. Restoration of quantum linearity requires a conceptual approach to hybrid classical-quantum coupling. Studies of the measurement problem and the quantum-classical transition point the way to a solution. It is based on a postulated mechanism of spontaneous quantum monitoring plus feedback. This approach eliminates Schrödinger cat states, takes quantum fluctuations into the account, and restores the linearity of quantum dynamics. Such conceptionally ’healthier’ semiclassical theory is captivating, exists in the Newtonian limit, but its relativistic covariance hits a wall. Here we will briefly recapitulate the concept and its realization in the nonrelativistic limit. We emphasize that the long-known obstacles to the relativistic extension lie in quantum foundations.

Continuous quantum measurement and feedback induce energy exchange between a dissipative qubit and a monitor even in the steady state, as a measurement backaction. Using the Lindblad equation, we identified the maximum and minimum values of the steady-state energy flow as the measurement and feedback states vary, and we demonstrate the qubit cooling induced by these processes. Turning our attention to quantum trajectories under continuous measurement and feedback, we observe that the energy flow fluctuates around the steady-state values. We reveal that the fluctuations are strongly influenced by the measurement backaction, distinguishing them from the standard Poisson noise typically observed in electronic circuits. Our results offer potential application in the development of quantum refrigerators controlled by continuous measurement and feedback, and provide deep insight into quantum thermodynamics from the perspective of fluctuation.

Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell’s Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell’s Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon’s memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon’s memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal: it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.

Quantum technologies and experiments often require preparing systems in low-temperature states. Here we investigate cooling schemes using feedback protocols modeled with a quantum Fokker-Planck master equation(QFPME) recently derived by Annby-Andersson etal. [Phys. Rev. Lett. 129, 050401 (2022)0031-900710.1103/PhysRevLett.129.050401]. This equationdescribes systems under continuous weak measurements, with feedback based on the outcome of these measurements. We apply this formalism to study the cooling and trapping of a harmonic oscillator for several protocols based on position and/or momentum measurements. We find that the protocols can cool the oscillator down to, or close to, the ground state for suitable choices of parameters. Our analysis provides an analytically solvable case study of quantum measurement and feedback and illustrates the application of the QFPME to continuous quantum systems.

Abstract As an homage to Quantum Energy Teleportation, we generalize the idea to arbitrary physical observables, not limited to energy, and prove a rigorous upper bound on the activated (“teleported”) quantity. The essence of this protocol is a quantum feedback control applied to an entangled ground state of a quantum many-body system. To illustrate the concept, we investigate a (1+1)-dimensional Dirac system and apply feedback control based on fermion chirality to activate electric current and charge. One of the most significant results is the creation of long-range correlations across the system after applying control operations only to one local site. Consequently but surprisingly, the induced charge susceptibility fully reconstructs the phase diagram, despite the model initially having no charge. Moreover, we find an activation of novel chiral dynamics induced by feedback control operations, which can be experimentally confirmed using trapped ions and neutral atoms.

A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of fresh qubits, alternative schemes which do not require measurements are possible. In such schemes, the error correction is realized via crafted coherent quantum feedback. We propose implementations of small measurement-free QEC schemes, which are fault tolerant to circuit-level noise. These implementations are guided by several heuristics to achieve fault tolerance: redundant syndrome information is extracted, and additional single-shot flag qubits are used. By carefully designing the circuit, the additional overhead of these measurement-free schemes is moderate compared to their conventional measurement and feed-forward counterparts. We highlight how this alternative approach paves the way towards implementing resource-efficient measurement-free QEC on neutral-atom arrays. Published by the American Physical Society 2024

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

In recent years, integrating quantum feedback mechanisms into thermal machines has gained attention due to its benefits in manipulating the system states and energy flows. This is particularly advantageous for quantum thermal transistors in preserving their inherent quantum properties as they lose the purity of the system states due to decoherence and relaxation from interactions with thermal baths, within the subsystems, and monitoring. In the literature, studies have demonstrated that preserving quantum coherence can enhance the performance of quantum thermal machines, improving their efficiency. In our paper, we present a model that proposes engineering baths to be equipped with detectors and a controller to enable feedback in a quantum thermal transistor that emulates a role played by a feedback resistor in an electronic transistor. We use the framework of quantum feedback control via weak monitoring. We modify the system evolution trajectories by using a weak monitoring record from a detector. By taking the ensemble average of these trajectories, we unveil the evolution of the system density matrix that corresponds to the Markovian dynamics of the transistor. This type of feedback introduces minimal perturbation to the system and, once tuned, enhances the system coherence that would otherwise degrade due to bath interactions. Furthermore, there will be no change in the relaxation times. The probabilities of population terms remain unchanged. We treat this an enhancement in the operational characteristics of the quantum thermal transistor as it maintains its quantum features with an added benefit of improved amplification capabilities.

Abstract A scheme is proposed to enhance quantum correlation, including entanglement and steering, for two magnon modes in a cavity‐magnon hybrid system through coherent quantum feedback. The hybrid system consists of a microwave cavity and two YIG spheres, which incorporates a nonlinear flux‐driven Josephson parametric amplifier in order for the generation of two photons within the cavity simultaneously. A quantum coherent feedback loop is used for the reduction of effective dissipation. By modulating feedback parameters, optimal bipartite and tripartite entanglement, as well as quantum steering are derived. Importantly, compared with the same setup without coherent feedback, the proposed scheme significantly improves quantum correlation. Furthermore, by optimizing the feedback reflectivity and the ratio of cavity‐magnon coupling strength, the enhancement of asymmetric steering can be controlled. Notably, incorporating the feedback loop effectively increase its robustness against thermal noise, thus the scheme offer better prospect for experimental development. This study paves the way for advancements in quantum information processing and quantum entanglement within cavity‐magnonics.

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.