Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization

Quantum Multiobservable Control

We present deterministic algorithms for the simultaneous control of an arbitrary number of quantum observables. Unlike optimal control approaches based on cost function optimization, quantum multiobservable tracking control (MOTC) is capable of tracking predetermined homotopic trajectories to target expectation values in the space of multiobservables. The convergence of these algorithms is facilitated by the favorable critical topology of quantum control landscapes. Fundamental properties of quantum multiobservable control landscapes that underlie the efficiency of MOTC, including the multiobservable controllability Gramian, are introduced. The effects of multiple control objectives on the structure and complexity of optimal fields are examined. With minor modifications, the techniques described herein can be applied to general quantum multiobjective control problems.Comment: To appear in Physical Review

Spatial Non-Locality Induced Non-Markovian EIT in a Single Giant Atom

In recent experiments, electromagnetically induced transparency (EIT) were observed with giant atoms, but nothing unconventional were found from the transmission spectra. In this letter, we show that unconventional EIT does exist in giant atoms, and indicate why it has not been observed so far. Different from these existing works, this letter presents a consistent theory including a real space method and a time delayed master equation for observing unconventional EIT. We discover that this phenomenon is a quantum effect which cannot be correctly described in a semi-classical way as those in recent works. Our theory shows that it can be observed when the time delay between two neighboring coupling points is comparable to the relaxation time of the atom, which is crucial for a future experimental observation. This new phenomenon results from inherent non-locality of the giant atom, which physically forces propagating fields to be standing waves in space and the atom exhibiting retardations in time. Our theory establishes a framework for application of nonlocal systems to quantum information processing.Comment: 6 pages, 3 figures, Comments are welcom

General unifying features of controlled quantum phenomena

Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the others. This work shows that all such scenarios inherently share the same fundamental control features residing in the topology of the landscape relating the target physical observable to the applied controls. This unified foundation may provide a basis for development of hybrid control schemes that would combine the advantages of the existing approaches to achieve the best overall performance.Comment: The published version (includes the supplementary material