Bounding fidelity in quantum feedback control: theory and applications to Dicke state preparation
arXiv:2503.19151 · doi:10.1088/2058-9565/ade55f
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.
21 pages, 6 figures. Close to published version
References in corpus (77)
- Cold atoms in cavity-generated dynamical optical potentials
- The maximum speed of dynamical evolution
- Preparation of Entangled States by Quantum Markov Processes
- Real-time quantum feedback prepares and stabilizes photon number states
- Fisher information and multiparticle entanglement
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Feedback-control of quantum systems using continuous state-estimation
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Quantum speed limits in open system dynamics
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Measurement-based quantum control of mechanical motion
- Real-time quantum error correction beyond break-even
- Real-time optimal quantum control of mechanical motion at room temperature
- Quantum control of a nanoparticle optically levitated in cryogenic free space
- Deterministic entanglement of superconducting qubits by parity measurement and feedback
- Boundary time crystals
- Colloquium: Quantum Batteries
- Generalized Geometric Quantum Speed Limits
- Deterministic Squeezed States with Joint Measurements and Feedback
- Reinforcement Learning with Neural Networks for Quantum Feedback
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- Stabilizing feedback controls for quantum systems
- Extracting work from quantum measurement in Maxwell demon engines
- Feedback-stabilization of an arbitrary pure state of a two-level atom
- Artificial Intelligence and Machine Learning for Quantum Technologies
- Deterministic Dicke state preparation with continuous measurement and control
- Spin squeezing via quantum feedback
- Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
- Tightening Quantum Speed Limits for Almost All States
- Multiparticle entanglement under the influence of decoherence
- When does reinforcement learning stand out in quantum control? A comparative study on state preparation
- Deep Reinforcement Learning for Quantum Gate Control
- A non-equilibrium superradiant phase transition in free space
- Generalizable control for quantum parameter estimation through reinforcement learning
- A discrete invitation to quantum filtering and feedback control
- On optimum Hamiltonians for state transformations
- Measurement Based Feedback Quantum Control With Deep Reinforcement Learning for Double-well Non-linear Potential
- Comparing and combining measurement-based and driven-dissipative entanglement stabilization
- Dissipation driven quantum phase transitions and symmetry breaking
- Noisy quantum metrology enhanced by continuous nondemolition measurement
- Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear Measurements
- Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing
- Action quantum speed limits
- Ultimate limits for quantum magnetometry via time-continuous measurements
- Quantum metrology with boundary time crystals
- Quantum control of atomic systems by time resolved homodyne detection and feedback
- Estimation of a classical parameter with gaussian probes: magnetometry with collective atomic spins
- Bell's inequality for conditional probabilities as a test for quantum-like behaviour of mind
- A Reinforcement Learning approach for Quantum State Engineering
- Learning feedback control strategies for quantum metrology
- Breaking Adiabatic Quantum Control with Deep Learning
- A Deterministic and Nondestructively-Verifiable Photon Number Source
- Quantum Speed Limits under Continuous Quantum Measurements
- Quantum cooling and squeezing of a levitating nanosphere via time-continuous measurements
- Daemonic ergotropy in continuously-monitored open quantum batteries
- Using Spontaneous Emission of a Qubit as a Resource for Feedback Control
- Conditional dynamics of optomechanical two-tone backaction-evading measurements
- Reinforcement learning-enhanced protocols for coherent population-transfer in three-level quantum systems
- Classifying global state preparation via deep reinforcement learning
- Quantum spin chain dissipative mean-field dynamics
- Determination of maximal Gaussian entanglement achievable by feedback-controlled dynamics
- Quantum Superposition State Production by Continuous Observations and Feedback
- Extreme Spin Squeezing from Deep Reinforcement Learning
- Dissipation-driven quantum phase transitions in collective spin systems
- A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback
- Non-markovian mesoscopic dissipative dynamics of open quantum spin chains
- Effects of dissipation in an adiabatic quantum search algorithm
- Unconditional mechanical squeezing via back-action evading measurements and non-optimal feedback control
- Quantum thermodynamics of boundary time-crystals
- Experimental simulation of daemonic work extraction in open quantum batteries on a digital quantum computer
- Linear feedback stabilization of a dispersively monitored qubit
- Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements
- Mechanical cooling and squeezing using optimal control
- Preparing Schrödinger cat states in a microwave cavity using a neural network
- Time-delayed quantum feedback and incomplete decoherence suppression with no-knowledge measurement
- Control limit on quantum state preparation under decoherence