Geometric approach to robust quantum control for time-varying noises

Quantum technologies are expected to revolutionze modern information processing industries.Almost all quntum technologies demand high-precision control of quantum systems.However,maintaining the high-precision against noises is rather difficult[1].This requirement calls for robust control pulse design that is insensitive to noises.For practical implementation,the control pulses need to be smoothly shaped and be able to tackle parametric uncertainties or time-varying noises with complicated frequency characteristics.

Deterministic Teleportation of an Arbitrary Two-Qubit State Via a One-Dimensional Four-Qubit Cluster State

This paper presents an approach to deterministically teleport an arbitrary two-qubit state through a one-dimensional four-qubit cluster state serving as a probabilistic quantum channel. The channel is modu- lated in advance to avoid damage to the original states in this scheme, which is caused by the inevitable failure of constructing a channel between the sender and the receiver. The scheme is flexible because the channel can be modulated either by the sender or by the receiver, with the option of deciding whether the sender or the receiver modulates the channel, according to the distribution of the available particle re- sources. The efficiency can be improved by reusing previously discarded results that may lead to a faithful channel. The scheme can be uniformly performed, so the design process can be greatly simplified to realize a reliable deterministic teleportation. Finally, the scheme is extended to deterministic teleportation of an arbitrary n-qubit state in a generalized form.

The modelling of quantum control systems

High-performance control of quantum dynamics is key to the development of quantum technologies.From quantum-state engineering to quantum metrology,theory and practice of quantum control enable robust and cheaper technologies for future industrial applications.Starting from fundamental matter–field interactions, we overview various approaches to modelling quantum control systems, in which control can be implemented by either changing field or material properties. These models are built in time or frequency domain and can be interconnected to form quantum feedback networks. This review can be taken as a useful reference for engineers to understand the quantum physics behind, or for physicists to resolve control problems from a control engineering point of view.

Optimal control of quantum systems with SU(1,1)dynamical symmetry

SU（1,1） dynamical symmetry is of fundamental importance in analyzing unbounded quantum systems in theoretical and applied physics. In this paper, we study the control of generalized coherent states associated with quantum systems with SU（1,1） dynamical symmetry. Based on a pseudo Riemannian metric on the SU（1,1） group, we obtain necessary conditions for minimizing the field fluence of controls that steer the system to the desired final state. Further analyses show that the candidate optimal control solutions can be classified into normal and abnormal extremals. The abnormal extremals can only be constant functions when the control Hamiltonian is non-parabolic, while the normal extremals can be expressed by Weierstrass elliptic functions according to the parabolicity of the control Hamiltonian. As a special case, the optimal control solution that maximally squeezes a generalized coherent state is a sinusoidal field, which is consistent with what is used in the laboratory.

Optimization Landscape of Quantum Control Systems

Optimization is ubiquitous in the control of quantum dynamics in atomic,molecular,and optical systems.The ease or difficulty of finding control solutions,which is practically crucial for developing quantum technologies,is highly dependent on the geometry of the underlying optimization landscapes.In this review,we give an introduction to the basic concepts in the theory of quantum optimal control landscapes,and their trap-free critical topology under two fundamental assumptions.Furthermore,the effects of various factors on the search effort are discussed,including control constraints,singularities,saddles,noises,and non-topological features of the landscapes.Additionally,we review recent experimental advances in the control of molecular and spin systems.These results provide an overall understanding of the optimization complexity of quantum control dynamics,which may help to develop more efficient optimization algorithms for quantum control systems,and as a promising extension,the training processes in quantum machine learning.

Preface

In the past decades, the ability of observing and manipulating quantum phenomena has been tremendously improved. It has advanced the thriving of quantum technologies with atomic, optical and solid-state systems.