Information flow and error scaling for fully-quantum control

Abstract

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behaviour of the optimal control error. Specifically, we prove that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes and can be applied to a very large class of platforms for controllable quantum devices.

9 pages, 4 figures

References in corpus (13)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Coherent quantum LQG control
• A Survey on Quantum Channel Capacities
• Modeling and Control of Quantum Systems: An Introduction
• Optimal Dynamical Decoherence Control of a Qubit
• Gaussian states in continuous variable quantum information
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Stabilizing Open Quantum Batteries by Sequential Measurements
• Quantum Feedback Control of Atomic Motion in an Optical Cavity
• Quantum Capacities of Channels with small Environment
• Donor spins in silicon for quantum technologies
• Optimal Quantum Filtering and Quantum Feedback Control
• Qubit quantum channels: A characteristic function approach

Cited by in corpus (4)

• One decade of quantum optimal control in the chopped random basis
• Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Experimental realization of optimal time-reversal on an atom chip for quantum undo operations