Extended techniques for feedback control of a single qubit

Quantum Control of a Single Qubit

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The ta...

Optimality of Feedback Control Strategies for Qubit Purification

Bellman equations for optimal feedback control of qubit states

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser’s amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of...

Quantum Feedback Control of a Solid-State Qubit

The principle of feedback control is used in a wide variety of physical and engineering problems. For example, it can be applied in a straightforward way to tune the oscillation phase of a harmonic oscillator in order to achieve a desired synchronization. An intriguing and fundamental question is whether continuous feedback can be used to control quantum systems; for instance, if it is possible...

Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations

The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this “instantaneous” process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously tra...