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International Conference Physics and Control

Feedback control of ensemble of HF quantum molecules

Mikhail S. Ananyevskiy

Published Oct 4, 2006• 0 citations
Publisher

Abstract

A new control law for energy stabilization for ensembles of quantum molecules is obtained. The semiclassical model of molecular dynamics onto the ground state is used. The range of the control pulse frequency is the parameter of algorithm. The computer simulation illustrates the efficiency of ensemble average energy stabilization for 200 fs laser pulse.

DOI
10.1109/phycon.2005.1514065

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A new control law for energy stabilization for ensembles of quantum molecules is obtained. The semiclassical model of molecular dynamics onto the ground state is used. The range of the control pulse frequency is the parameter of algorithm. The computer simulation illustrates the efficiency of ensemble average energy stabilization for 200 fs laser pulse.
We introduce two approaches to the synthesis of the optimized schemes of dissociation control of diatomic molecules. The first one bases on the early introduced speed-gradient algorithms of the quantum control. We use the semi classical model of molecular dynamics onto the ground state. The introduced algorithm is a robust and it has only one tuning parameter. The numerical results of the control of the predissociation of iodine molecule illustrate the high possibility of the dissociation for 100 fs laser pulse. The second approach bases on quantum model of dissociation through B excited electronic state. This model doesn't assume the solving of any time-depended equations. The optimized scheme of iodine dissociation with different nuclear isotopes is obtained. The best isotope separation achieves up to 300 fs with 80% efficiency.
Molecules under the inuence of light can be used to perform quantum computational operations when their vibrational or rotational quantum states are coherently controlled. An analysis is presented of quantum computation within the vibrational degrees of freedom of a polyatomic molecule. A set of 2n vibrational states covering a range of energies is used to encode n qubits in place of n separate degrees of freedom. Computer simulations are used to demonstrate the capacity of a shaped laser pulse to execute 4-qubit quantum computational algorithms with high delity on gas phase thiophosgene. An alternative light-molecule system using terahertz pulses on gas phase D3O+ is also analyzed and found to have the capability of performing 2-qubit operations. Simulations of closed loop experiments in coherent control are presented, and elements of the experimental procedure are tested to demonstrate how intramolecular vibrational relaxation (IVR) may be slowed in the ground state vibrational energy levels of gas phase thiophosgene.
Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an eigenstate of a given Hamiltonian, assuming that the lower energy eigenstates are known. To this aim, we propose a new design methodology that combines the layer wise construction of the quantum circuit in feedback-based quantum algorithms with a new feedback law based on a new Lyapunov function to assign the quantum circuit parameters. We present two approaches for evaluating the circuit parameters: one based on the expectation and overlap estimation of the terms in the feedback law and another based on the gradient of the Lyapunov function. We demonstrate the algorithm through an illustrative example and through an application in quantum chemistry. To assess its performance, we conduct numerical simulations and execution on IBM's superconducting quantum computer.
The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024