Quantum feedback: Theory, experiments, and applications

Abstract

The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to-date, and its applications. In the last few years there has been rapid experimental progress in the ability to realize quantum measurement and control of mesoscopic systems. We expect that the next few years will see further rapid advances in the precision and sophistication of feedback control protocols realized in the laboratory.

A feedback scheme for control of single electron transport

“…The feedback discussed here consists of an active scheme where measurement results are used to modulate system and/or bath parameters during the entire time evolution . This clearly involves some intrinsically classical, stochastic signals even if the system to be controlled is fully quantum.…”

Unitarity, feedback, interactions—dynamics emergent from repeated measurements

“…In such a case the potential terms in equation (D3) would read~X å Äĉ S S i j j i j s i j s , , 1 2 and could induce interactions even entangling the two systems. With such measurements the interaction terms could arise in the regime of effective unitarity, section 3.1, and would thus differ from the feedback schemes where the conditional state exhibits entanglement or where non-unitary terms are present [5,6,45,54,55]. The above assumption regarding interactions, and its role, is fully analogous to the linearity assumption in the case of feedback discussed at the end of section 3.3.…”

“…The resulting state of the ancillae then determines the effective potential which arises for the system from the next interaction ÄŜ M j j . Thus, for a suitable choice of the interactions and the state of the ancillae, an operation on the system is effectively performed that depends on its quantum state-that is coherent feedback [5,6,32,45] Therefore, independently of the weak or strong interaction regime, the state of ancillae or the repetition rate of the measurements, with the present model of ancillae-system interactions, feedback-control of the system cannot be realized without introducing dissipation lower bounded according to equation (3.12). See also [46,47] for a comparison between coherent quantum feedback and the measurement-based feedback.…”

Coherent control in quantum transport: amplification, filtering and switching at finite bias

“…In 2010, Brandes [2] first proposed the use of quantum feedback control [3,4,5] to manipulate the flow of transport electrons and described a feedback scheme to suppress fluctuations in the inherently stochastic flow of electrons through a quantum dot. This work spawned a number of theoretical proposals to use feedback to produce a range of interesting transport effects such as stabilisation of nonequillibrium quantum states [6,7,8] and the realisation of a mesoscopic Maxwell's demon [9,10,11].…”