Quantum proportional-integral (PI) control
arXiv:2007.13853 · doi:10.1088/1367-2630/abc464
Abstract
Feedback control is an essential component of many modern technologies and provides a key capability for emergent quantum technologies. We extend existing approaches of direct feedback control in which the controller applies a function directly proportional to the output signal (P feedback), to strategies in which feedback determined by an integrated output signal (I feedback), and to strategies in which feedback consists of a combination of P and I terms. The latter quantum PI feedback constitutes the analog of the widely used proportional-integral feedback of classical control. All of these strategies are experimentally feasible and require no complex state estimation. We apply the resulting formalism to two canonical quantum feedback control problems, namely, generation of an entangled state of two remote qubits, and stabilization of a harmonic oscillator under thermal noise under conditions of arbitrary measurement efficiency. These two problems allow analysis of the relative benefits of P, I, and PI feedback control. We find that for the two-qubit remote entanglement generation the best strategy can be a combined PI strategy when the measurement efficiency is less than one. In contrast, for harmonic state stabilization we find that P feedback shows the best performance when actuation of both position and momentum feedback is possible, while when only actuation of position is available, I feedback consistently shows the best performance, although feedback delay is shown to improve the performance of a P strategy here.
arXiv commentPublished version
References in corpus (44)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Entanglement of a Pair of Quantum Bits
- Feedback-control of quantum systems using continuous state-estimation
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Measurement-based quantum control of mechanical motion
- Quantum feedback control and classical control theory
- Coherent quantum LQG control
- Adaptive homodyne measurement of optical phase
- Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits
- Continuous quantum error correction via quantum feedback control
- Feedback cooling of a single trapped ion
- Feedback cooling of a nanomechanical resonator
- Feedback-stabilization of an arbitrary pure state of a two-level atom
- Analysis of Lyapunov Method for Control of Quantum Systems
- Analysis of Lyapunov Method for Control of Quantum States
- Past quantum states
- Sliding Mode Control of Two-Level Quantum Systems
- Dynamical creation of entanglement by homodyne-mediated feedback
- Quantum Filtering (Quantum Trajectories) for Systems Driven by Fields in Single Photon States and Superposition of Coherent States
- Quantum Feedback Control of Atomic Motion in an Optical Cavity
- Time-Symmetric Quantum Theory of Smoothing
- Risk-Sensitive Optimal Control of Quantum Systems
- Continuous quantum nondemolition feedback and unconditional atomic spin squeezing
- Optimal control of entanglement via quantum feedback
- Mirror quiescence and high-sensitivity position measurements with feedback
- Quantum error correction for continuously detected errors
- Laser cooling of a nanomechanical oscillator to the zero-point energy
- Rapid State-Reduction of Quantum Systems Using Feedback Control
- Near ground-state cooling of two-dimensional trapped-ion crystals with more than 100 ions
- Quantum risk-sensitive estimation and robustness
- Quantum State Smoothing
- Macroscopic mechanical oscillators at the quantum limit using optomechanical cooling
- Feedback cooling of atomic motion in cavity QED
- Coherent controllers for optical-feedback cooling of quantum oscillators
- Near-ground-state cooling of atoms optically trapped 300nm away from a hot surface
- Chip-to-chip entanglement of transmon qubits using engineered measurement fields
- Deterministic generation of remote entanglement with active quantum feedback
- Efficient feedback controllers for continuous-time quantum error correction
- Continuous joint measurement and entanglement of qubits in remote cavities
- Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
- Linear feedback stabilization of a dispersively monitored qubit
- Smoothing of Gaussian quantum dynamics for force detection
- Feedback-assisted ponderomotive squeezing
- Non-Markovian Quantum Feedback Networks II: Controlled Flows
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