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arXiv:1407.0654

Cavity QED Photons for Quantum Information Processing

Moteb M. Alqahtani, Mark S. Everitt, B. M. Garraway

Published Jul 2, 2014• 0 citations
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Abstract

Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities. In this way the information has been stored in cavities and the off-resonant atomic levels have been eliminated by the semi-classical theory of an effective two-level Hamiltonian. A further semi-classical model, namely the spin-$J$ model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multilevel multiphoton models have been performed. The combination of the two semi-classical models has been employed to address two-level, three-level, four-level, and even five-level configurations. The impact of decoherence processes on the fidelity of the iSWAP and the Fredkin gates has been studied.

DOI
10.48550/arxiv.1407.0654

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Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities. In this way the information has been stored in cavities and the off-resonant atomic levels have been eliminated by the semi-classical theory of an effective two-level Hamiltonian. A further semi-classical model, namely the spin-JJJ model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multilevel multiphoton models have been performed. The combination of the two semi-classical models has been employed to address two-level, three-level, four-level, and even five-level configurations. The impact of decoherence processes on the fidelity of the iSWAP and the Fredkin gates has been studied.
Based on a multi-mode multi-level Jaynes-Cummings model and multi-photon resonance theory, a set of universal two-qubit and three-qubit gates has been realized where dual-rail qubits are encoded in cavities. In this way, the information has been stored in cavities and the off-resonant levels have been eliminated by the theory of an effective two-level Hamiltonian. A further model, namely the spin-J model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multilevel multi-photon models have been performed. The combination of the two models has been employed to address two-level, three-level, four-level, and even five-level configurations. Considering the present cavity-QED experiments, several numerical simulations have been designed in order to check the robustness of the logic gates to variations in experimentally important parameters including the coupling constants and the detunings. Finally, based on Liouville's equation, and the wave-function treatments, the impact of decoherence processes on the fidelity of the qubit states in the iSWAP and the Fredkin gates has been studied. This thesis may have applications to quantum information processing, involving logic with simple quantum bits, with the possible application to the building of a quantum computer.
Abstract Based on a cavity QED framework, we theoretically describe a universal set of logic gates which are implemented by passing a multi-level atom initially in its ground state through a multi-mode cavity. The qubits are encoded on the cavity modes and the atom plays the role of an ancilla which will not be entangled with the final result of a gate operation. We apply the multiphoton resonance theory of Shore to develop effective two- and three-level Hamiltonians, so that the proper values for detunings, coupling coefficients, and interaction times for gate operations can be determined. This enables us to examine a faster iSWAP gate than our previous study and to examine numerically the effects of decoherence on both the iSWAP gate and our previously presented Fredkin gate which used the same multi-mode approach. We also present results that show how conditional measurements of the ancilla atom can improve gate fidelities in these cases.
We develop a theory for the interaction of multilevel atoms with multimode cavities yielding cavity-enhanced multiphoton resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realized when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the Fredkin gate and iswap operation; the system seems promising for scalability.
Due to the improvement within cavity quantum electrodynamics experiments during the last decades, what was former seen as 'toy models' are today realized in laboratories. A controlled isolated coherent evolution of one or a few atoms coupled to a single mode inside a cavity is achievable. Such systems are well suited for studying purely quantum mechanical effects, and also for performing quantum gates, necessary for quantum computing. The Jaynes-Cummings model has served as a theoretical description of the interaction. However, as the experimental techniques are improved, for example, atom cooling, the use of multi-level atoms or multi-modes and driving of atoms or elds by external lasers, extensions of the original Jaynes-Cummings model are needed. In this thesis we study some of these extended models, and in particular multi-level models, time-dependent models and quantized motion models. Both analytical and numerical analysis are considered. The two-level structure of the Jaynes-Cummings model leads to applications of known solvable time-dependent two-level Schrödinger equations. In other cases, di erent forms of adiabatic approximate solutions are used, and with the analytically solvable models, the amplitudes of non-adiabatic contributions may be estimated. For higher dimensional systems, STIRAP and multi-STIRAP methods are applied. It is shown how the time-dependent models may be used for preparation of various kinds of non-classical states, and also to generate universal sets of quantum gates, both on atomic and eld qubits. When the atoms are cooled to very low temperatures, their velocities must be treated quantum mechanically, and we have studied the dynamics of such cases for di erent coupling shapes. Again numerical and analytical approaches have been used and compared, wave-packet propagations of the atom, approaching and traversing the cavity, have been performed. For periodic couplings, standing wave cavity modes, the dynamics has been described by e ective parameters; group velocity or atomic index of refraction and effective mass. Tunneling resonances for ultra cold atoms have been exhibited in the STIRAP models for certain initial conditions.
A novel scheme is proposed for realizing quantum entanglement, quantum information transfer and a set of universal quantum gates with superconducting-quantum-interference-device (SQUID) qubits in cavity QED. In the scheme, the two logical states of a qubit are the two lowest levels of the SQUID. An intermediate level of the SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. The method presented here does not create finite intermediate-level population or cavity-photon population during the operations. Thus, decoherence due to spontaneous decay from the intermediate levels is minimized and the requirement on the quality factor of the cavity is greatly loosened.