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Optics Express

Robust hyperparallel photonic quantum entangling gate with cavity QED

Bao‐Cang Ren, Fu‐Guo Deng

Published May 2, 2017• 69 citations
Publisher

Abstract

Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlled-phase-flip gate for a two-photon system in both the polarization and spatial-mode degrees of freedom (DOFs), in which the noise caused by the inequality of two reflection coefficients can be depressed efficiently. This gate doubles the quantum entangling operation synchronously on a photon system and can reduce the quantum resources consumed largely and depress the photonic dissipation efficiently, compared with the two cascade quantum entangling gates in one DOF. It has a near unit fidelity. Moreover, we show that the balance condition can be obtained in both the weak coupling regime and the strong coupling regime, and the high-fidelity quantum gate operation is easier to be realized in the balance condition than the ones in the ideal condition in experiment.

DOI
10.1364/oe.25.010863

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Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlled-phase-flip gate for a two-photon system in both the polarization and spatial-mode degrees of freedom (DOFs), in which the noise caused by the inequality of two reflection coefficients can be depressed efficiently. This gate doubles the quantum entangling operation synchronously on a photon system and can reduce the quantum resources consumed largely and depress the photonic dissipation efficiently, compared with the two cascade quantum entangling gates in one DOF. It has a near unit fidelity. Moreover, we show that the balance condition can be obtained in both the weak coupling regime and the strong coupling regime, and the high-fidelity quantum gate operation is easier to be realized in the balance condition than the ones in the ideal condition in experiment.
Encoding computing qubits in multiple degrees of freedom (DOFs) of a photonic system allows hyperparallel quantum computation to enlarge channel capacity with less quantum resource, and constructing high-fidelity hyperparallel quantum gates is always recognized as a fundamental prerequisite for hyperparallel quantum computation. Herein, we propose an approach for implementing a high-fidelity photonic hyperparallel controlled-phase-flip (CPF) gate working with polarization, spatial-mode, and frequency DOFs, through utilizing the practical interaction between the single photon and the diamond nitrogen vacancy (NV) center embedded in the cavity. Particularly, the desired output state of the gate without computation errors coming from the practical interaction is obtained, and the robust fidelity is guaranteed in the nearly realistic condition. Meanwhile, the requirement for the experimental realization of the gate is relaxed. In addition, this approach can be generalized to complete the high-fidelity photonic three-DOF hyperparallel CPFN gate and parity-check gate. These interesting features may make the present scheme have potential for applications in the hyperparallel quantum computation.
We present the dipole induced transparency (DIT) of a diamond nitrogen-vacancy center embedded in a photonic crystal cavity coupled to two waveguides, and it is obvious with the robust and flexible reflectance and transmittance difference of circularly polarized lights between the uncoupled and the coupled cavities even in the bad cavity regime (the Purcell regime). With this DIT, we propose two universal hyperparallel hybrid photonic quantum logic gates, including a hybrid hyper-controlled-not gate and a hybrid hyper-Toffoli gate, on photon systems in both the polarization and the spatial-mode degrees of freedom (DOFs), which are equal to two identical quantum logic gates operating simultaneously on the systems in one DOF. They can be used to perform more quantum operations with less resources in the quantum information protocols with multiqubit systems in several DOFs, which may depress the resources consumed and the photonic dissipation. Moreover, they are more robust against asymmetric environment noise in the weak-coupling regime, compared with the integration of two cascaded quantum logic gates in one DOF.
The two or more degrees of freedoms (DOFs) of photon systems are very useful in hyperparallel photonic quantum computing to accomplish more quantum logic gate operations with less resource, and depress photonic dissipation noise in quantum information processing. We present some flexible and adjustable schemes for hybrid hyper-controlled-not (hyper-CNOT) gates assisted by low-Q cavities, on the two-photon systems in both the spatial-mode and the polarization DOFs. These hybrid spatial-polarization hyper-CNOT gates consume less quantum resource and are more robust against photonic dissipation noise, compared with the integration of two cascaded CNOT gates in one DOF. Besides, simultaneous counter-propagation of two photons economize extremely the operation time in the whole process of our schemes. Moreover, these quantum logic gates are more feasible for fast quantum operations in the weak-coupling region of the low-Q cavities with current experimental technology, which are much different from strong-coupling cases of the high-Q ones.
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.
Usually, the hyperparallel quantum computation can speed up quantum computing, reduce the quantum resource consumed largely, resist to noise, and simplify the storage of quantum information. Here, we present the first scheme for the self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom of photon systems simultaneously. It can prevent bit-flip errors from happening with an imperfect nonlinear interaction in the nearly realistic condition. We give the way to design the universal hyperparallel photonic quantum controlled-NOT (CNOT) gate on a two-photon system, resorting to the nonlinear interaction between the circularly polarized photon and the electron spin in the quantum dot in a double-sided microcavity system, by taking the imperfect interaction in the nearly realistic condition into account. Its self-error-corrected pattern prevents the bit-flip errors from happening in the hyperparallel quantum CNOT gate, guarantees the robust fidelity, and relaxes the requirement for its experiment. Meanwhile, this scheme works in a failure-heralded way. Also, we generalize this approach to achieve the self-error-corrected hyperparallel quantum CNOTN gate working on a multiple-photon system. These good features make this scheme more useful in the photonic quantum computation and quantum communication in the future.
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.