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Journal of Physics B Atomic Molecular and Optical Physics

Cavity QED photons for quantum information processing

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

Published Aug 19, 2022• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/ac864f

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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.
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.
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.
We describe a quantum phase gate in which the two qubits are represented by the photons in the two modes of the cavity field. The gate is implemented by passing a three-level atom in a cascade configuration through the cavity. The upper levels of the atom are resonant with one of the cavity modes whereas the lower levels are appropriately detuned from the other mode of the cavity. A $\ensuremath{\pi}$ phase shift is introduced when there is one photon each in the two modes and the atom is initially in the ground state. We also discuss the one-bit unitary gate in such a system and discuss potential applications.
We solve the Jaynes-Cummings Hamiltonian with time-dependent coupling parameters under the dipole and rotating-wave approximations for a three-dimensional photonic crystal (PC) single-mode cavity with a sufficiently high-quality Q factor. We then exploit the results to show how to create a maximally entangled state of two atoms and how to implement several quantum logic gates: a dual-rail Hadamard gate, a dual-rail NOT gate, and a SWAP gate. The atoms in all of these operations are syncronized, which is not the case in previous studies of PCs [J. Mod. Opt.48, 1495 (2001); Eur. Phys. J. D10, 285 (2000); Eur. Phys. J. D18, 247 (2002)]. Our method has the potential for extension to N-atom entanglement, universal quantum logic operations, and the implementation of other useful, cavity QED-based quantum information processing tasks.
A two-qubit quantum swap gate scheme based on coherent state qubit is proposed in cavity quantum electrodynamics system. Our scheme adopt the interaction between the Λ-type atomic ensemble and the two-mode optical cavity, and the swap gate can be realized directly only one step, so as to save a lot of quantum resources and reduce the number of single qubit rotation operations in the actual quantum information processing. It is found that under the condition of large detuning limit, the excited states of atoms are adiabatically eliminated, and the decoherence caused by the spontaneous emission of atoms is effectively suppressed. All atoms in the optical cavity are universally addressed, which reduces the experimental operation difficulty of the scheme. The fidelity of the quantum logic gate is maintained at a very high level when the photon loss of the cavity field is considered. Compared with the single-atom scheme, it is found that the atom-cavity interaction time required by the atomic ensemble scheme is inversely proportional to the number of atoms, so that the speed of the quantum logic gate can be increased by N times. Therefore, in principle, as long as enough atoms interacting with the optical field, an effective coupling of any atom-cavity field can be generated, which is conducive to selecting the appropriate quantum gate operation time in practical operation and effectively avoiding decoherence.