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arXiv:2306.16565 · Physical Review A

Parallel multi-two-qubit swap gate via quantum nondemolition interaction of orbital-angular-momentum light and an atomic ensemble

E. N. Bashmakova, E. A. Vashukevich, T. Yu. Golubeva

Published Jan 23, 2024• 4 citations
arXivHTMLPDF

Abstract

Nowadays, the quantum swap gate has become an integral part of quantum computing, so the investigation of methods for its realization seems to be an important practical problem for various quantum-optical and information applications. In the present paper, we propose a scheme for performing a swap logic operation in discrete variables in the framework of quantum nondemolition interaction between an atomic ensemble and a multimode light with orbital angular momentum. We discuss in detail the procedure for revealing two-qubit closed subsystems on a set of atomic and field states for different values of the driving field orbital momentum. We also demonstrate the possibility of implementing a parallel multi-two-qubit quantum swap gate.

DOI
10.1103/physreva.109.012428

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Nowadays, the quantum swap gate has become an integral part of quantum computing, so the investigation of methods for its realization seems to be an important practical problem for various quantum-optical and information applications. In the present paper, we propose a scheme for performing a swap logic operation in discrete variables in the framework of quantum nondemolition interaction between an atomic ensemble and a multimode light with orbital angular momentum. We discuss in detail the procedure for revealing two-qubit closed subsystems on a set of atomic and field states for different values of the driving field orbital momentum. We also demonstrate the possibility of implementing a parallel multi-two-qubit quantum swap gate.
Abstract To date, two-qubit quantum logic gates have become an essential part of quantum computing. The study of methods for their implementation is an important practical problem for various quantum optical and information applications. In this paper, we have considered a protocol for multimode quantum non-demolition interaction between an atomic ensemble and multimode light with orbital angular momentum in order to analyze the applicability of this protocol in discrete variables computing. We have developed a multimode interaction Hamiltonian and analyzed the dynamics of field and atomic variables depending on the structure of the driving field. We discuss in detail the procedure for separating qubit noninteracting subsystems on a set of atomic and field modes for various values of the orbital angular momentum of the driving field. Such a procedure helps to reduce the considered protocol to the parallel evolution of two-qubit closed systems.
The paper presents an analysis of entangling and nonlocal operations in a quantum nondemolition (QND) interaction between multimode light with orbital angular momentum and an atomic ensemble. A protocol consists of two QND operations with rotations of quadratures of atomic spin coherence and light between them. This protocol provides a wide range of two-qubit operations, while the multimode nature of the chosen degrees of freedom allows the implementation of parallel operations over multiple two-qubit systems. We have used the formalism of equivalence classes and local invariants to evaluate the properties of two-qubit transformations. It is shown that, when selecting suitable values of the governing parameters, such as the duration of each of the two QND interactions and the rotation angles of the qubits, the protocol allows to realize a deterministic nonlocal SWAP operation and entangling SWAP\sqrt{\text{SWAP}}SWAP​ operation with probability 13\frac{1}{3}31​.
To date, two-qubit quantum logic gates have become an essential part of quantum computing. The study of methods for their implementation is an important practical problem for various quantum optical and information applications. In this paper, we have considered a protocol for multimode quantum non demolition interaction between an atomic ensemble and multimode light with orbital angular momentum in order to analyze the applicability of this protocol in discrete variables computing. We have developed a multimode interaction Hamiltonian and analyzed the dynamics of field and atomic variables depending on the structure of the driving field. We discuss in detail the procedure for separating qubit noninteracting subsystems on a set of atomic and field modes for various values of the orbital angular momentum of the driving field. Such a procedure helps to reduce the considered protocol to the parallel evolution of two-qubit closed systems.
The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate SWAPdαSWAP^α_dSWAPdα​. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.
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.
We propose and experimentally demonstrate an optimized setup to implement quantum controlled-NOT operation using polarization and orbital angular momentum qubits. This device is more adaptive to inputs with various polarizations, and can work both in classical and quantum single-photon regime. The logic operations performed by such a setup not only possess high stability and polarization-free character, they can also be easily extended to deal with multi-qubit input states. As an example, the experimental implementation of generalized three-qubit Toffoli gate has been presented.