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.
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.
Accurate rotation–vibration energy levels and transition dipoles of the molecule thiophosgene are used to model the execution of quantum gates with shaped laser pulses. Qubits are encoded in 2 n vibrational computing states on the ground electronic surface of the molecule. Computations are carried out by cycling amplitude between these computing states and a gateway state with a shaped laser pulse. The shaped pulse that performs the computation is represented by a physical model of a 128–1024 channel pulse shaper. Pulse shapes are optimized with a standard genetic algorithm, yielding experimentally realizable computing pulses. The robustness of optimization is studied as a function of the vibrational states selected, rotational level structure, additional vibrational levels not assigned to the computation, and compensation for laser power variation across a molecular ensemble.
For practical realization of quantum information processing we need a quantum system that provides reliable preparation of the initial state, high-fidelity quantum gate operations, error tolerance, readout of the result of quantum computation and scalability of the system to increase the number of qubits. In this dissertation we show how these requirements can be addressed for molecular quantum computer. For computational study of quantum information processing with molecules we employ thiophosgene (SCCl2) molecule that has been used as a test system for quantum control experiments [Mol. Phys. 105, 1999 (2007)]. We investigate the gateway scheme of control in which transitions between the vibrational states that encode qubits are only allowed through the intermediate “gateway” state in the B electronic state. This scheme of control provides reliable preparation of the initial qubit state and allows using UV/vis laser pulses. We demonstrate that high-fidelity quantum gates are possible to achieve in molecular quantum computer. The optimal control theory is employed to obtain a shape of laser pulse that performs CNOT gate with ~0.9999 fidelity. Analysis of frequency profile of the optimal pulse shows that preparation of the high-fidelity computational pulse requires only 64 frequency channels. Error tolerance of the computational pulse is studied by modifying amplitudes and phases of frequency components. It is shown that gate fidelity remains high after small modifications are introduced to the optimal pulse. The scheme of readout of quantum information using quantum beat spectroscopy is proposed. The quantum beat signal is obtained from excitation of the final superposition of the qubit states to a readout state in the B electronic state with a time-delayed pulse. We find that fitting the quantum beat signal with a standard fitting expression produces a phase error and propose a new accurate expression that includes phase correction term. The system of two atomic ions trapped in a double-well potential is also studied as a first step towards scalable quantum computation with trapped molecular ions. The rigorous computational treatment of the system provides explanation of the vibrational energy transfer between the ions in terms of wave packet dynamics in the accurate asymmetric potential.
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favorable; sources for decoherence can be eliminated. A complete set of one- and two-quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation.
Any real system, no matter how well isolated, unavoidably interacts with the environment. This interaction makes the evolution of a quantum system nonunitary and destroys the coherence of quantum superpositions. This process, known as decoherence, is widely regarded as the most important and fundamental obstacle to the practical realization of quantum information processing. On the other hand, the objectives of quantum control are predicated on the ability to manipulate the system coherently over a period of time. Quantum control has been applied successfully to several experimental systems and coupling such a controlled system to an environment makes the study of coherence loss possible. The standard model of decoherence is formulated in terms of a system, defined by the observables that can be measured, and a reservoir, de¯ned by those degrees of freedom that are not accessed by observation. The vibrational and rotational degree of freedom of diatomic molecules form an experimental model of such a system and bath 1. The nature of the ro-vibrational coupling does not allow a Decoherence Free Subspace, instead we try to identify a Decoherence Resistant Subspace using closed loop control. We set up a learning control loop experiment to monitor the coherence in a vibrational wavepacket, consisting of about 6 vibrational states of the A(1Σ+g ) electronic state, excited by a shaped, ultrashort optical pulse, and then to determine the pulse shape that yielded the longest coherence lifetime. The coherence of the vibrational wavepacket was monitored by measuring the fluorescence quantum beats from the outer turning point of the wave packet's trajectory. The closed loop controller altered the shape of the driving optical pulse to maximize the the depth of modulation of the quantum beats at a prescribed time after excitation, within the constraints of the laser system. The outcome of this closed loop control experiment shows an improvement of the beat decay constant of about 60%, as shown in Fig. (1), a result which occurs for several di®erent pulse shapes. Our experiments show that a number of interesting decoherence-resistant excitations exist. The nature of the dephasing was examined theoretically. Using measured optical pulse shapes, we simulated numerically the molecular wavepacket in the limit of perturbation theory. The experiment and simulations show that there are di®erent mechanisms contributing to the decoherence resistant excitation. The shaped pulse reduces the °uctuations in the wave packet spatial extent, which in turn changes the system reservoir coupling. Other components of the optimal pulse are a sequence of pulses that creates constructive interference of the vibrational wavepacket at the desired time, and chirp which compensates for the anharmonicity of the adiabatic potential. The experimental results show general agreement with numerical simulations. We conclude that wavepackets resistant to dephasing do exist,and that learning algorithms provide an effcient means for finding them.
My thesis focuses on theoretical studies in the molecular quantum computing with vibrational qubits. We studied how the molecular vibrational properties affect the fidelity of the logic gates. Our approach is to encode states of the quantum information register into the vibrational eigenstates of a molecule and use the shaped laser pulse (femtosecond, infrared) to control the vibrational state-to-state transition. By using the Optimal Control Theory to shape a femtosecond laser and numerical propagation of laser-driven vibrational wave packets, we analyzed how the vibrational properties of a two-qubit system affect the accuracy of the quantum gates and how to effectively control the vibrational state-to-state transitions. From these studies, we found the anharmonicities are very important for the control of the vibrational state-to-state transitions and an intricate interplay between the frequencies and anharmonicities in the two-qubit system leads to the occurrence of resonances between different transitions in the vibrational manifold. Such resonances cause "leakage" of population into other vibrational states and hinder the control. From theoretical analysis of resonances, we formulate several criteria for selection of molecule for implementation of the vibrational two-qubit system. These criteria can help experimentalists to choose the best molecules to achieve accurate qubit transformations in the experiment.