Coherent control of single electrons: a review of current progress

Abstract: In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches which have been developed over the last ten years in order to gain full control over a propagating single electron in a solid state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single electron sources which are compatible with integrated single electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments about the new physics that emerges using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

• The paper reviews advanced experimental techniques for coherently controlling single electrons in semiconductor systems.
• It discusses the implementation of quantum protocols like Bloch sphere rotations and quantum rail encoding using flying electrons.
• The study highlights progress in developing single-electron sources and detectors crucial for scalable quantum information processing.

Coherent Control of Single Electrons: A Review of Current Progress

The landscape of quantum information processing and solid-state physics has undergone significant advancements through the manipulation of single-electron quantum states. The paper "Coherent control of single electrons: a review of current progress" provides an exhaustive account of the methodologies and experiments aimed at controlling single-electron propagation in solid-state systems, with particular focus on its implications for quantum information processing.

Overview of Approaches and Experimental Implementations

The paper begins with a discussion on the rapid downsizing in semiconductor components reaching dimensions that allow electron transport at a single-electron level. Quantum dots and nanowires within semiconductor heterostructures are highlighted as primary systems for confining and manipulating electrons. Integral to the creation of practical single-electron circuits is the coherent transport and interconnection of electrons between different functional components, analogous to optical photons in quantum optical circuits.

A critical component within these architectures is the ability to code qubit information in either the charge or spin degrees of freedom, with emphasis on experiments using "flying electrons" as conveyors of quantum information. The paper outlines the quantum protocols necessary to achieve these control mechanisms, such as quantum rail encoding and single-qubit rotations using tunnel-coupled nanostructures.

Theoretical Framework for Flying Qubits

The authors elaborate on the theoretical underpinnings required for the realization of flying qubits. Single-qubit operations are discussed in terms of Bloch sphere rotations, facilitated by electronic circuits acting as coherent manipulators. The paper illustrates the crucial components of quantum networks using these qubits conditioned by precise electron wave phases and quantum interference effects, such as the Aharonov-Bohm effect.

Experimental Realizations

There is an assessment of significant experiments achieving coherent transport in quantum Hall regimes, where quantum point contacts act as beam splitters in Mach-Zehnder interferometers. The paper contrasts this with experimental implementations at low magnetic fields which, though historically more complex due to backscattering effects, offer potential conducive to scalability.

Additionally, the review covers advances utilizing tunnel-coupled wire interferometry, emphasizing the need for pseudo-two-port architectures to achieve interference similar to optical systems even at zero magnetic field. The utility of controllable electrostatic gates for modulating phase and achieving precise single qubit control is highlighted.

Advances in Single-Electron Sources and Detectors

The development of single-electron sources is critical for experimental realizations at the single-electron level, and the review details innovations such as the mesoscopic capacitor and non-adiabatic quantised charge pumps. The coherent and reliable emission of single electrons is essential for experiments simulating quantum optics, while measurement challenges in detecting these electrons with single-shot precision are addressed through proposals for ultra-sensitive qubit-based electrometers.

Implications and Future Directions

The review outlines the implications of these developments for both fundamental science and practical applications in quantum computing. It proposes that continued refinements in synchronizing and enhancing the fidelity of these single-electron circuits could lead to their integration in scalable quantum information processing systems, possibly achieving architectures that rival photonic systems. Future challenges identified include overcoming coherence losses due to electron interactions and improving detection capabilities that support full single-electron quantum coherence.

In sum, the paper presents a comprehensive assessment of the current capabilities in coherent single-electron control. It examines the intricate balance required between understanding theoretical possibilities and addressing practical challenges to leverage this technology for future quantum computing applications.