Limits of optimal control yields achievable with quantum controllers
arXiv:1412.5287 · doi:10.1103/PhysRevA.91.042327
Abstract
In quantum optimal control theory, kinematic bounds are the minimum and maximum values of the control objective achievable for any physically realizable system dynamics. For a given initial state of the system, these bounds depend on the nature and state of the controller. We consider a general situation where the controlled quantum system is coupled to both an external classical field (referred to as a classical controller) and an auxiliary quantum system (referred to as a quantum controller). In this general situation, the kinematic bound is between the classical kinematic bound (CKB), corresponding to the case when only the classical controller is available, and the quantum kinematic bound (QKB), corresponding to the ultimate physical limit of the objective's value. Specifically, when the control objective is the expectation value of a quantum observable (a Hermitian operator on the system's Hilbert space), the QKBs are the minimum and maximum eigenvalues of this operator. We present, both qualitatively and quantitatively, the necessary and sufficient conditions for surpassing the CKB and reaching the QKB, through the use of a quantum controller. The general conditions are illustrated by examples in which the system and controller are initially in thermal states. The obtained results provide a basis for the design of quantum controllers capable of maximizing the control yield and reaching the ultimate physical limit.
10 pages, 5 figures
References in corpus (63)
- Mixed State Entanglement and Quantum Error Correction
- An Open-System Quantum Simulator with Trapped Ions
- Control of quantum phenomena: Past, present, and future
- Quantum Thermodynamic Cycles and quantum heat engines
- Maximal work extraction from quantum systems
- Quantum control theory and applications: A survey
- Real-time quantum feedback prepares and stabilizes photon number states
- Entanglement generated by dissipation and steady state entanglement of two macroscopic objects
- Quantum heat engines and refrigerators: Continuous devices
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Dissipative production of a maximally entangled steady state
- Stabilizing entanglement autonomously between two superconducting qubits
- Cavity-assisted quantum bath engineering
- Demonstrating a Driven Reset Protocol of a Superconducting Qubit
- Coherent-feedback quantum control with a dynamic compensator
- All-optical versus electro-optical quantum-limited feedback
- Feedback control of a solid-state qubit using high-fidelity projective measurement
- Feedback cooling of a single trapped ion
- Ground state cooling of mechanical resonators
- An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
- Quantum thermodynamic cooling cycle
- Experimental feedback control of quantum systems using weak measurements
- Advantages of Coherent Feedback for Cooling Quantum Oscillators
- Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback
- Quantum control by von Neumann measurements
- Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
- Optimal refrigerator
- An information theoretical analysis of quantum optimal control
- Stabilizing a Bell state of two superconducting qubits by dissipation engineering
- Boundary of Quantum Evolution under Decoherence
- Robust control of quantum gates via sequential convex programming
- Experimental demonstration of coherent feedback control on optical field squeezing
- Controllability of open quantum systems with Kraus-map dynamics
- Degrees of controllability for quantum systems and applications to atomic systems
- Simultaneous cooling of an artificial atom and its neighboring quantum system
- Exploring constrained quantum control landscapes
- Feedback Cooling of a Single Neutral Atom
- Control Landscapes for Observable Preparation with Open Quantum Systems
- Singularities of Quantum Control Landscapes
- Tunable coupling to a mechanical oscillator circuit using a coherent feedback network
- Quantum Coherent Nonlinear Feedbacks with Applications to Quantum Optics on Chip
- Characterization of the Critical Submanifolds in Quantum Ensemble Control Landscapes
- Search complexity and resource scaling for the quantum optimal control of unitary transformations
- Exploring Quantum Control Landscapes: Topology, Features, and Optimization Scaling
- Measurement driven quantum evolution
- Quantum control and the Strocchi map
- Quantum resources for purification and cooling: fundamental limits and opportunities
- Observation-assisted optimal control of quantum dynamics
- Criteria for reachability of quantum states
- Bayesian feedback control of a two-atom spin-state in an atom-cavity system
- Incoherent Control of Locally Controllable Quantum Systems
- Feedback Control Using Only Quantum Back-Action
- Optimal Efficiency of a Noisy Quantum Heat Engine
- Characterization of control noise effects in optimal quantum unitary dynamics
- A superconducting microwave multivibrator produced by coherent feedback
- Exploring the top and bottom of the quantum control landscape
- Searching for quantum optimal controls in the presence of singular critical points
- Comment on "Are There Traps in Quantum Control Landscapes?"
- The role of controllability in optimizing quantum dynamics
- Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
- Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability
- General unifying features of controlled quantum phenomena
- Maintaining Quantum Coherence in the Presence of Noise through State Monitoring