Quantum control theory and applications: A survey

This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective, some references are added, published versio

Control Paradigms for Quantum Engineering

We give an overview of different paradigms for control of quantum systems and their applications, illustrated with specific examples. We further discuss the implications of fault-tolerance requirements for quantum process engineering using optimal control, and explore the possibilities for architecture simplification and effective control using a minimum number of simple switch actuators.Comment: 6 pages, presented at ISCCP08 in Malta, to appear in IEEE Proceeding

Sampled-data design for robust control of a single qubit

This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for guiding the design of unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.Comment: 33 pages, 5 figures, minor correction

Sliding Mode Control of Two-Level Quantum Systems

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system's state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We propose a controller design method using the Lyapunov methodology and periodic projective measurements. In particular, we give conditions for designing such a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.Comment: 29 pages, 4 figures, accepted by Automatic

Towards understanding two-level-systems in amorphous solids -- Insights from quantum circuits

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered -- what are these two-level defects? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to two-level defects within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects -- observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.Comment: 34 pages, 7 figures, 1 tabl

Integrated Photonic Sensing

Loss is a critical roadblock to achieving photonic quantum-enhanced technologies. We explore a modular platform for implementing integrated photonics experiments and consider the effects of loss at different stages of these experiments, including state preparation, manipulation and measurement. We frame our discussion mainly in the context of quantum sensing and focus particularly on the use of loss-tolerant Holland-Burnett states for optical phase estimation. In particular, we discuss spontaneous four-wave mixing in standard birefringent fibre as a source of pure, heralded single photons and present methods of optimising such sources. We also outline a route to programmable circuits which allow the control of photonic interactions even in the presence of fabrication imperfections and describe a ratiometric characterisation method for beam splitters which allows the characterisation of complex circuits without the need for full process tomography. Finally, we present a framework for performing state tomography on heralded states using lossy measurement devices. This is motivated by a calculation of the effects of fabrication imperfections on precision measurement using Holland-Burnett states.Comment: 19 pages, 7 figure

Experimental study of the quantum phase-slip effect in NbN nanowires

Coherent quantum phase-slip (QPS) in a superconducting nanowire is the dual phenomenon to the well-known Josephson effect. Josephson junctions form the basis of superconducting electronic circuits with a wide range of applications, and each of those circuits has a corresponding dual quantum phase-slip device with a dual purpose. Examples that draw particular attention are a new quantum standard of electric current, and a quantum phase-slip qubit. The aim of this project is to develop methods of design, fabrication, and measurement of quantum phase-slip nanowires, and to demonstrate the potential of these devices for technological application. In our experiments we incorporate NbN nanowires into a superconducting loop and bias the loop with a magnetic flux. The state of the nanowire-embedded loop is then read out by coupling to a high quality coplanar waveguide resonator. In this thesis we present the results of two such experiments. First, we fabricated NbN nanowires using a neon focused-ion-beam, and measured their properties at T=300 mK. Periodic tuning of the resonant frequency of the readout resonator revealed that magnetic flux is transferred to the interior of the loop with flux-quantum-periodicity. Our measurements confirm that the flux-quantum transfer is mediated by incoherent quantum phase-slips occurring in the nanowires, and that these incoherent QPS can be fully controlled with an external bias. In the second experiment, nanowire-embedded NbN loops were fabricated by electron-beam lithography and cooled to T=10 mK. The resonant frequency tuning exhibited avoided crossings, which is evidence of coherent coupling between the resonator and a coherent quantum two-level system. We numerically fit these avoided crossings to the Jaynes-Cummings model to extract the properties of the two-level system, and find a good fit with the design parameters of our nanowire qubit. Finally we discuss whether the observation of coherent dynamics is evidence of coherent QPS in the EBL-fabricated nanowire