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arXiv:quant-ph/0507268 · Journal of Physics A Mathematical and General

Adiabatic quantum computing with phase modulated laser pulses

Debabrata Goswami

Published Sep 7, 2005• 10 citations
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Abstract

Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.

DOI
10.1088/0305-4470/38/38/l02

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Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.
A robust implementation of quantum logical gates for a multilevel system is possible through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. Selective population inversion and Hamiltonian evolution with time through ultrafast pulse shaping techniques essentially amount to adiabatic quantum computing (AQC) instead of the standard unitary transformation. An important aspect of the AQC model is in addressing the atomic or molecular ensemble and hence in robust implementation. We argue that experimental demonstrations of selective population transfer through adiabatic rapid passage form useful adiabatic quantum computing logic. Similarly, a simple Hadamard operation can be demonstrated with phase-modulated laser pulses. Finally, we present a framework to efficiently solve approximate Euclidean Traveling Salesman Problem (Approx-TSP) with bounded error in the AQC model. We present an efficient and intuitive encoding for Approx-TSP in a quantum computing paradigm. Optical approaches to quantum computing have the potential to be used in a distributive sense to defray the present caveat of limited resources and scalability. We present how we make use of such schemes towards practicality issues in AQC. As far as we know, our results are the first realistic demonstration of the possibility of using ensemble states for AQC in multilevel systems.
Selective control of decoherence is demonstrated for a multilevel system by generalizing the instantaneous phase of any chirped pulse as individual terms of a Taylor series expansion. In the case of a simple two-level system, all odd terms in the series lead to population inversion, while the even terms lead to self-induced transparency. These results also hold for multiphoton transitions that do not have any lower-order photon resonance or any intermediate virtual state dynamics within the laser pulse width. Such results form the basis of a robustly implementable CNOT gate.
This thesis is based upon the work published in the following two articles entitled: Robust Operation of a Universal Set of Logic Gates for Quantum Computation using Adiabatic Population Transfer between Molecular Levels [37], and Piecewise Adiabatic Passage with a Series of Femtosecond Pulses [54]. Both papers involve using the concept of a quantum control phenomenon, known as adiabatic passage in different manners, in order to achieve particular goals. In the first paper we present a robust construction of a set of logic gates operating on a system of qubits encoded in the ro-vibrational eigenstates of an Na₂ molecule using the optical Adiabatic Population Transfer (APT) method. We demonstrate the operation of a complete universal gate-set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to dealing with a larger number of qubits. The second line of research developed from the desire to merge the robustness of an adiabatic process, as presented in the previous paper, with the speed and additional level of control available by using pulse shaping techniques of broadband pulses. Therein we develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is found to be robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.
We develop protocols for high-fidelity single-qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures where direct transitions between logical states are either vanishingly small or nonexistent; in such systems traditional approaches cannot be implemented. Prime examples are superconducting fluxonium qubits, which have highly localized states, and AMO systems, where there are no dipole allowed transitions between the ground states encoding the logical states. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modeling the effects of decoherence, we explore the trade-off between speed and robustness that is inherent to shortcuts-to-adiabaticity approaches.
Based on the semi-classical theory of the interaction between light and matter, we propose an effective scheme for describing the realization of single quantum gates. The rigorous analytical solution for the resonant system, in which the double ultra-short powerful laser pulses with accurately controllable relative phase difference will interact with the atoms, is obtained by solving the time-dependent Schrödinger equation. According to the corresponding solution, we deduce the systematic matrix expression of unitary transformation. Universal quantum logic gates are all implemented theoretically by means of regulating properly the laser pulses' intensity and its relative phase difference as well as the optic detuning. This method also proves practical in terms of its comparably easier manipulation.