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arXiv:2405.08141 · Physical Review A

Parallel two-qubit entangling gates via a quantum nondemolition interaction controlled by rotation

E. A. Vashukevich, T. Yu. Golubeva

Published Sep 18, 2024• 1 citation
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Abstract

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 $\sqrt{\text{SWAP}}$ operation with probability $\frac{1}{3}$.

DOI
10.1103/physreva.110.032616

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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​.
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.
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.
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.
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.
Abstract Quantum gate teleportation enables spatially separated parties to implement nonlocal quantum operations using preshared entanglement, local operations, measurement, and classical communication. Here, we present a two-branch entanglement-assisted coherent-control architecture for the deterministic remote implementation of nonlocal two-qubit gates. In this architecture, the two parties coherently select between two pairs of local unitary operations acting on their respective input qubits, a structure that can be naturally encoded through spatial-path superposition. The protocol is formulated at the operator level, allowing deterministic operation to be established independently of the input-state parametrization and making its scope explicit. For two-qubit unitary targets, we show that the deterministic branch conditions restrict the nonlocal domain of the balanced two-branch ansatz: apart from local product operations, any implementable nonlocal unitary must be locally unitarily equivalent to the CNOT/CZ class. We construct explicit CNOT and controlled- Z realizations as two representatives of this unique nonlocal equivalence class. We also introduce a photonic path-encoding and destructive branch-readout scheme in which spatial path encodes the coherent-control degree of freedom and polarization carries the computational qubits, illustrating how the proposed architecture can be physically encoded.
The power of a quantum circuit is determined through the number of two-qubit entangling gates that can be performed within the coherence time of the system. In the absence of parallel quantum gate operations, this would make the quantum simulators limited to shallow circuits. Here, we propose a protocol to parallelize the implementation of two-qubit entangling gates between multiple users which are spatially separated, and use a commonly shared spin chain data-bus. Our protocol works through inducing effective interaction between each pair of qubits without disturbing the others, therefore, it increases the rate of gate operations without creating crosstalk. This is achieved by tuning the Hamiltonian parameters appropriately, described in the form of two different strategies. The tuning of the parameters makes different bilocalized eigenstates responsible for the realization of the entangling gates between different pairs of distant qubits. Remarkably, the performance of our protocol is robust against increasing the length of the data-bus and the number of users. Moreover, we show that this protocol can tolerate various types of disorders and is applicable in the context of superconductor-based systems. The proposed protocol can serve for realizing two-way quantum communication.