Optimal control theory for unitary transformations

2002

Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The approach is illustrated in the implementation of one and two qubits gates in model molecular systems.

Physical Review Letters, 2002

Quantum computation is based on implementing selected unitary transformations representing algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The approach is independent of the physical implementation of the quantum computer and it is illustrated for one and two qubit gates in model molecular systems, where only part of the Hilbert space is used for computation.

2017

Using quantum optimal control to drive intramolecular vibrational redistribution and to perform quantum computing December 2017-Université Libre de Bruxelles-Ludovic Santos Quantum optimal control theory is applied to find optimal pulses for controlling the motion of an ion and a molecule for two different applications. Those optimal pulses enable the control of the dynamics of the system by driving the atom or the molecule from an initial state to desired states. The evolution equations obtained by means of the quantum optimal control theory are resolved iteratively using a monotonic convergent algorithm. A number of simulation parameters are varied in order to get the optimal pulses including the duration of the pulses, the time step of the time grid, a penalty factor that limits the maximal intensity of the fields, and a guess pulse which is used to start the optimal control. The optimal pulses obtained for each application are analyzed by Fourier transform, and also by looking at the time evolution of the populations that they generate in the system.

arXiv (Cornell University), 2007

Finding control laws (pulse sequences) that can compensate for dispersions in parameters which govern the evolution of a quantum system is an important problem in the fields of coherent spectroscopy, imaging, and quantum information processing. The use of composite pulse techniques for such tasks has a long and widely known history. In this paper, we introduce the method of Fourier synthesis control law design for compensating dispersions in quantum system dynamics. We focus on system models arising in NMR spectroscopy and NMR imaging applications.

Physical Review A, 1998

We construct a Hamiltonian for the generation of arbitrary pure states of the quantized electromagnetic field. The proposition is based upon the fact that a unitary transformation for the generation of number states has been already found. The general unitary transformation here obtained, would allow the use of nonlinear interactions for the production of pure states. We discuss the applicability of this method by giving examples of generation of simple superposition states. We also compare our Hamiltonian with the one resulting from the interaction of trapped ions with two laser fields. 42.50.Ct, 42.50.Dv

Physical Review A, 2008

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 where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2) × SU(2) × U(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.

Physical Review A, 1993

The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method, a requisite external field is obtained to track exactly a prescribed molecular objective expectation value as a function of time. Applications to diatomic and polyatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for position and energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

2001

Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with finite rise and decay times or Gaussian wavepackets. The technique is applied to find control schemes that achieve population transfers for pure-state systems, complete inversions of

Physical Review A, 2011

We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a V-type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5P 1/2 → 5P 3/2 transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.