Related papers: Minimum time generation of SU(2) transformations w…
For the time optimal control on an invariant system on SU(2), with two independent controls and a bound on the norm of the control, the extremals of the maximum principle are explicit functions of time and the resulting differential…
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We…
In this work we derive a lower bound for the minimum time required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the…
We consider a quantum control problem involving a spin-1/2 particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the x-y plane, serves as a control…
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…
In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case…
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
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…
We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used…
In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
Quantum ensemble systems arise in a variety of applications, including NMR spectroscopy and robust quantum control. While their theoretical properties have been extensively studied, relatively little attention has been given to the explicit…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
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 propose an analysis of the time-optimal control of SU(2) quantum operations. By using the Pontryagin Maximum Principle, we show how to determine the optimal trajectory reaching a given target state. Explicit analytical solutions are…
We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…
We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the…