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Physical Review A

Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities

Tao Li, Gui‐Lu Long

Published Aug 31, 2016• 97 citations
Publisher

Abstract

We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnot${}^{N}$ gate on $N+1$ hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.

DOI
10.1103/physreva.94.022343

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We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnotN{}^{N}N gate on N+1N+1N+1 hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.
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.
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.
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.
We propose deterministic schemes for controlled-NOT (CNOT), Toffoli, and Fredkin gates between flying photon qubits and the collective spin wave (magnon) of an atomic ensemble inside double-sided optical microcavities. All the gates can be accomplished with 100% success probability in principle and no additional qubit is required. Atomic ensemble is employed so that light-matter coupling is remarkably improved by collective enhancement. We qualified the performance of the gates and the results show that they can be faithfully constituted with current experimental techniques.
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
Photonic hyper-parallel quantum information processing (QIP) can simplify the quantum circuit and improve the information-processing speed, as well as reduce the quantum resource consumption and suppress the photonic dissipation noise. Here, utilizing the singly charged semiconductor quantum dot (QD) inside single-sided optical microcavity as the potentially experimental platform, we propose five schemes for heralded four-qubit hyper-controlled-not (hyper-CNOT) gates, covering all cases of four-qubit hyper-CNOT gates operated on both the polarization and spatial-mode degrees of freedom (DoFs) of a two-photon system. The novel heralding mechanism improves the fidelity of each hyper-CNOT gate to unity in principle without the strict restriction of strong coupling. The adaptability and scalability of the schemes make the hyper-CNOT gates more accessible under current experimental technologies. These heralded high-fidelity photonic hyper-CNOT gates can therefore have immense utilization potentials in high-capacity quantum communication and fast quantum computing, which are of far-reaching significance for QIP.