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Journal of the Optical Society of America B

Hyper-parallel nonlocal CNOT operation assisted by quantum-dot spin in a double-sided optical microcavity

Meng-Fan Chen, Ping Zhou, Qi Lan, Xiang-Qi Lu

Published Nov 10, 2023• 6 citations
Publisher

Abstract

Implementation of controlled-NOT (CNOT) operation between different nodes in a quantum communication network nonlocally plays an important role in distributed quantum computation. We present a protocol for implementation of hyper-parallel nonlocal CNOT operation via hyperentangled photons simultaneously entangled in spatial-mode and polarization degrees of freedom (DOFs) assisted by quantum-dot spin in a double-sided optical microcavity. The agent Alice lets photons traverse the double-sided optical microcavity sequentially and applies single-qubit measurements on the electron and the hyperentangled photon. The agent Bob first performs corresponding unitary operations according to Alice’s measurement results on his hyperentangled photon, and then lets photons traverse the double-sided optical microcavity sequentially and performs the single-qubit measurements on the electron and the hyperentangled photon. The hyper-parallel nonlocal CNOT operation can be implemented simultaneously in spatial-mode and polarization DOFs if Alice performs single-qubit operations in accordance with Bob’s measurement results. The protocol has the advantage of having high channel capacity for long-distance quantum communication by using a hyperentangled state as the quantum channel.

DOI
10.1364/josab.505732

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Implementation of controlled-NOT (CNOT) operation between different nodes in a quantum communication network nonlocally plays an important role in distributed quantum computation. We present a protocol for implementation of hyper-parallel nonlocal CNOT operation via hyperentangled photons simultaneously entangled in spatial-mode and polarization degrees of freedom (DOFs) assisted by quantum-dot spin in a double-sided optical microcavity. The agent Alice lets photons traverse the double-sided optical microcavity sequentially and applies single-qubit measurements on the electron and the hyperentangled photon. The agent Bob first performs corresponding unitary operations according to Alice’s measurement results on his hyperentangled photon, and then lets photons traverse the double-sided optical microcavity sequentially and performs the single-qubit measurements on the electron and the hyperentangled photon. The hyper-parallel nonlocal CNOT operation can be implemented simultaneously in spatial-mode and polarization DOFs if Alice performs single-qubit operations in accordance with Bob’s measurement results. The protocol has the advantage of having high channel capacity for long-distance quantum communication by using a hyperentangled state as the quantum channel.
Implementing three-qubit Toffoli gates nonlocally plays an important role in quantum communication networks and distributed quantum computation. Most of previous protocols for implementing quantum Toffolis gate consider only implementing Toffoli gates with one degree of freedom. In this paper, we present a scheme for parallel implementation of nonlocal Toffoli gates in polarization and spatial-mode degrees of freedom assisted by quantum dots inside a double-side optical microcavity. Alice and Bob let photons traverse the double-side optical microcavity sequentially and perform single-particle measurements on electron spin in quantum dots and the entangled photons. Charlie performs single-particle measurements and applies the corresponding unitary operation in polarization and spatial-mode degrees of freedom according to Alice and Bob’s measurement results. Alice and Bob can implement hyper-parallel nonlocal Toffoli gates by performing unitary operations according to Charlie’s measurement result. This protocol has the advantage of having high channel capacity by the hyperentangled state as the quantum channel.
Implementing CNOT operation nonlocally is one of central tasks in distributed quantum computation. Most of previously protocols for implementation quantum CNOT operation only consider implement CNOT operation in one degree of freedom(DOF). In this paper, we present a scheme for nonlocal implementation of hyper-parallel CNOT operation in polarization and spatial-mode DOFs via hyperentanglement. The CNOT operations in polarization DOF and spatial-mode DOF can be remote implemented simultaneously with hyperentanglement assisited by cross-Kerr nonlinearity. Hyper-parallel nonlocal CNOT gate can enhance the quantum channel capacity for distributed quantum computation and long-distance quantum communication. We discuss the experiment feasibility for hyper-parallel nonlocal gate. It shows that the protocol for hyper-parallel nonlocal CNOT operation can be realized with current technology.
Remote implementation of nonlocal quantum gates between different nodes in quantum communication network plays an important role in distributed quantum computation. Compared to protocol for nonlocal implementation of quantum operation in one degree of freedom (DoF), the protocol for parallel remote implementation of nonlocal operations simultaneously in two DoFs has the advantage of having high channel capacity. Under the balance condition of diamond nitrogen-vacancy center coupled to a single-side optical microcavity, we present a protocol for remote implementation of robust hyperparallel nonlocal operation in polarization, time-bin DoFs. Alice and Bob let photons pass through the diamond nitrogen-vacancy center system successively, perform single-qubit measurement on the entangled photons and the electrons. The robust nonlocal CNOT operation can be simultaneously implemented by applying unitary operations in accordance with the measurement results. The protocol has the advantage of transmitting less entangled photons for remote implementation of nonlocal CNOT operations in two DoFs. Moreover, the protocol is more convenient in application since the noise in the protocol for hyperparallel nonlocal CNOT operation via diamond nitrogen-vacancy center can be efficiently depressed.
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF.
To date, all work concerning the construction of quantum logic gates, an essential part of quantum computing, has focused on operating in one degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of achieving scalable photonic quantum computing based on two DOFs for quantum systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating in both the spatial mode and polarization DOFs for a photon pair simultaneously, using the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a one-side optical microcavity as a result of cavity quantum electrodynamics. With this hyper-CNOT gate and linear optical elements, two-photon four-qubit cluster entangled states can be prepared and analyzed, which give an application to manipulate more information with less resources. We analyze the experimental feasibility of this hyper-CNOT gate and show that it can be implemented with current technology.
Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm.