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arXiv:2004.02495 · Annalen der Physik

Implementing a Two‐Photon Three‐Degrees‐of‐Freedom Hyper‐Parallel Controlled Phase Flip Gate Through Cavity‐Assisted Interactions

Hai‐Rui Wei, Wen‐Qiang Liu, Ning‐Yang Chen

Published Mar 1, 2020• 14 citations
arXivHTMLPDF

Abstract

Abstract Hyper‐parallel quantum information processing is a promising and beneficial research field. Herein, a method to implement a hyper‐parallel controlled‐phase‐flip (hyper‐CPF) gate for frequency‐, spatial‐, and time‐bin‐encoded qubits by coupling flying photons to trapped nitrogen vacancy (NV) defect centers is presented. The scheme, which differs from their conventional parallel counterparts, is specifically advantageous in decreasing against the dissipate noise, increasing the quantum channel capacity, and reducing the quantum resource overhead. The gate qubits with frequency, spatial, and time‐bin degrees of freedom (DOF) are immune to quantum decoherence in optical fibers, whereas the polarization photons are easily disturbed by the ambient noise.

DOI
10.1002/andp.201900578

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Abstract Hyper‐parallel quantum information processing is a promising and beneficial research field. Herein, a method to implement a hyper‐parallel controlled‐phase‐flip (hyper‐CPF) gate for frequency‐, spatial‐, and time‐bin‐encoded qubits by coupling flying photons to trapped nitrogen vacancy (NV) defect centers is presented. The scheme, which differs from their conventional parallel counterparts, is specifically advantageous in decreasing against the dissipate noise, increasing the quantum channel capacity, and reducing the quantum resource overhead. The gate qubits with frequency, spatial, and time‐bin degrees of freedom (DOF) are immune to quantum decoherence in optical fibers, whereas the polarization photons are easily disturbed by the ambient noise.
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.
Abstract The construction of a near‐deterministic photonic hyperparallel quantum Fredkin (hyper‐Fredkin) gate is investigated for a three‐photon system with the optical property of a diamond nitrogen vacancy center embedded in an optical cavity (cavity‐NV center system). This hyper‐Fredkin gate can be used to perform double Fredkin gate operations on both the polarization and spatial‐mode degrees of freedom (DOFs) of a three‐photon system with a near‐unit success probability, compared with those on the double three‐photon systems in one DOF. In this proposal, the hybrid quantum logic gate operations are the key elements of the hyper‐Fredkin gate, and only two cavity‐NV center systems are required. Moreover, the possibility of constructing a high‐fidelity and high‐efficiency hyper‐Fredkin gate in the experimental environment of a cavity‐NV center system is discussed, which may be used to implement high‐fidelity photonic computational tasks in two DOFs with a high efficiency.
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.
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.
Abstract By harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.