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We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…
Optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving…
We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms. We derive an explicit formula to compute the minimum time required to steer…
We study the interplay between rotating wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time-independent…
We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic…
A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
In this paper we consider the minimum time population transfer problem for a two level quantum system driven by {\em two} external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave…
In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description…
Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is \change{placed} on the dependence on the maximum control…
Finding minimal time and establishing the structure of the corresponding optimal controls which can transfer a given initial state of a quantum system into a given target state is a key problem of quantum control. In this work, this problem…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By…
Optical techniques have been employed to coherently control the quantum transport through nanojunctions. Conventional works on optical control of quantum transport usually applied a tailored electrical pulses to perform specific tasks. In…
We present a constructive control scheme for solving quantum state engineering problems based on a parametrization of the state vector in terms of complex hyperspherical coordinates. Unlike many control schemes based on factorization of…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…