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AIP conference proceedings

Adiabatic Quantum Computation: Coherent Control Back Action

Debabrata Goswami

Published Jan 1, 2006• 3 citations
Publisher

Abstract

Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments.

DOI
10.1063/1.2400899

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Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments.
Quantum interference between multiple excitation pathways can be used to cancel the couplings to the unwanted, nonradiative channels resulting in robustly controlling decoherence through adiabatic coherent control approaches. We propose a useful quantification of the two-level character in a multilevel system by considering the evolution of the coherent character in the quantum system as represented by the off-diagonal density matrix elements, which switches from real to imaginary as the excitation process changes from being resonant to completely adiabatic. Such counterintuitive results can be explained in terms of continuous population exchange in comparison to no population exchange under the adiabatic condition.
In the past two decades many schemes to actively control the dynamical evolution of a quantum system have been proposed and established. We focus attention on the use of assisted adiabatic processes to generate selected target states with high efficiency. Specific control protocols that fall in this category are sometimes called shortcuts to adiabaticity. We review two assisted adiabatic population transfer schemes, the counter-diabatic and fast-forward protocols, with the intent of calling attention to their conceptual basis and applications to real systems, specifically vibrational energy transfer in polyatomic molecules and manipulation of Bose-Einstein (BEC) condensates. The particular applications of the counter-diabatic and fast-forward protocols to improving the efficiency of population transfer between vibrational states of a polyatomic molecule that we have studied are (i) selective vibrational energy transfer in the nonrotating thiophosgene (SCCl2) molecule and (ii) enhancing the yield of HNC in the driven rotation free isomerization reaction HCN→CNH. A major component of our considerations concerns reduction of the degradation of population transfer efficiency within a subset of states that is generated by coupling of the subset of states to a manifold of background states. We have examined the influence of a manifold of background vibrational states on population transfer within a subset of embedded vibrational states, and on how that influence can be suppressed. We emphasize that any control protocol must be designed to minimize interference between the background states and excitations within the selected subset of states that are used to define initial and target states. We have also examined the application of the fast-forward protocol to the transport of population between sites of a BEC in an optical lattice. Through the applications we illustrate how the theoretical framework of an assisted adiabatic process depends on the character of the system studied, on the available control parameters, on the constraints imposed by the experimental setting, on the efficiency of population transfer (fidelity) to be achieved, and on the stability of the control process with respect to the variation of the external control fields.
The merging of coherent control (CC) and adiabatic passage (AP) and the type of problems that can be solved using the resulting coherently controlled adiabatic passage (CCAP) method are discussed. The discussion starts with the essence of CC as the guiding of a quantum system to arrive at a given final state via a number of different quantum pathways. The guiding is done by ``tailor-made'' external laser fields. Selectivity in a host of physical and chemical processes is shown to be achieved by controlling the interference between such quantum pathways. The AP process is then discussed, in which a system is navigated adiabatically along a single quantum pathway, resulting in a complete population transfer between two energy eigenstates. The merging of the two techniques (CCAP) is shown to achieve both selectivity and completeness. Application of CCAP to the solution of the nondegenerate quantum control problem is first discussed and shown that it is possible to completely transfer population from an initial wave packet of arbitrary shape, composed of a set of nondegenerate energy eigenstates, to a final arbitrary wave packet, also composed of nondegenerate states. The treatment is then extended to systems with degenerate states and shown how to induce isomerization between the broken-symmetry local minima of a Jahn-Teller Al3O{\mathrm{Al}}_{3}\mathrm{O}Al3​O molecule. These approaches can be further generalized to situations with many initial, intermediate, and final states and applied to quantum coding and decoding problems. CCAP is then applied to cyclic population transfer (CPT), induced by coupling three states of a chiral molecule in a cyclic fashion, $\ensuremath{\mid}1⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}2⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}3⟩\ensuremath{\leftrightarrow}\ensuremath{\mid}1⟩$. Interference between two adiabatic pathways in CPT allows for a complete population transfer, coupled with multichannel selectivity, by virtue of its phase sensitivity. CPT can be used to show the purification of mixtures of right-handed and left-handed chiral molecules. Finally, quantum-field coherent control is introduced, where CCAP is extended to the use of nonclassical light. This emerging field may be used to generate new types of entangled radiation-matter states.
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.
We derive the driving potential that accelerates adiabatic population transfer from an initial state to a target state in a lattice system without unwanted excitation of other states by extending to discrete systems the fast-forward theory of adiabatic transfer. As an example, we apply the theory to a model that describes a Bose-Einstein condensate in a quasi-one-dimensional optical lattice, and show that modulation of the tilting of the lattice potential can transfer the population of the Bose-Einstein condensate from site to site with high fidelity and without unwanted excitations.