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International Journal of Quantum Information

ON THE PRACTICALITY OF ADIABATIC QUANTUM COMPUTING WITH OPTICAL SCHEMES

Debabrata Goswami

Published Feb 1, 2007• 2 citations

Abstract

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.

DOI: 10.1142/s0219749907002621

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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.

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.

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.

We present a robust construction of a set of logic gates operating on a system of qubits encoded in the rovibrational eigenstates of an

{\mathrm{Na}}_{2}

molecule using the optical adiabatic population transfer (APT) phenomenon. 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 deal with a larger number of qubits. With the aid of the set of gates thus shown we may construct pulse sequences for a wide class of quantum logic operations. We also show how to produce a representation of Bell states from a representation of product states with essentially perfect fidelity. Our scheme can be realized in all diatomic and polyatomic molecules that possess easily accessible and well characterized excited electronic states.

The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a

Λ

-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.