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Laser Physics

Universal photonic three-qubit quantum gates with two degrees of freedom assisted by charged quantum dots inside single-sided optical microcavities

Bo-Yang Xia, Cong Cao, Yu‐Hong Han, Ru Zhang

Published Jul 3, 2018• 28 citations
Publisher

Abstract

Abstract Although universal quantum computation can be realized with two-qubit controlled-not (CNOT) gates and single-qubit rotations, it would be convenient to have resource-efficient and robust multiqubit quantum gates in practical quantum information processing. Here we present two new schemes to determinately implement three-qubit Toffoli gate and Fredkin gate on photon systems with two degrees of freedom (DOFs), assisted by charged quantum dots (QDs) inside single-sided optical microcavities. In contrast to the traditional Toffoli and Fredkin gates operating in photonic one DOF, the gates presented here with two DOFs can reduce the photon numbers required to implement the gate operations. Compared with the ones synthesized by CNOT and single-qubit gates, the present gates can reduce the complexity in experiment. Our schemes exploit the robust giant circular birefringence induced by a single-electron spin in a QD-cavity system, which do not require photon indistinguishability or photon interference as demanded by other schemes using linear optics. Moreover, additional ancillary photons are not required in the schemes. We discuss the feasibility of our schemes, concluding that they can be realized with current or near-future technologies.

DOI
10.1088/1555-6611/aac904

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Abstract Semiconductor quantum‐dot (QD) spins hold great promise in quantum information science and technology. The implementation of high‐fidelity quantum gates on QD‐spin qubits is of great importance. Here, two schemes are presented to implement two universal quantum controlled gates, that is, the two‐qubit controlled‐not gate and the three‐qubit Toffoli gate, on stationary electron‐spin qubits in QDs inside single‐sided optical microcavities, based on the cavity‐assisted photon scattering under the balance condition. Compared with the previous schemes based on the ideal giant circular birefringence, the present schemes use the balance condition of the single‐sided QD‐cavity system, which can be achieved in both the weak‐ and strong‐coupling regimes of cavity quantum electrodynamics. Under the balance condition, the noise caused by the unbalanced reflectance between the coupled and uncoupled QD‐cavity systems can be efficiently depressed, so that the fidelity of each quantum gate operation can be increased to unity in principle. The schemes exhibit the possibility of realizing high‐fidelity and scalable quantum computing with single QD spins and single photons using the feasible and robust light–matter quantum interface. These high‐fidelity quantum controlled gates can lead to more efficient construction of quantum circuits for quantum computing, and provide a convenient avenue for quantum networking.
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.
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.
Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics. We design the compact quantum circuits for implementing universal and deterministic quantum gates for electron-spin systems, including the two-qubit CNOT gate and the three-qubit Toffoli gate. They are compact and economic, and they do not require additional electron-spin qubits. Moreover, our devices have good scalability and are attractive as they both are based on solid-state quantum systems and the qubits are stationary. They are feasible with the current experimental technology, and both high fidelity and high efficiency can be achieved when the ratio of the side leakage to the cavity decay is low.
It is desirable to implement an efficient quantum information process demanding fewer quantum resources. We designed two compact quantum circuits for determinately implementing four-qubit Toffoli and Fredkin gates on single-photon systems in both the polarization and spatial degrees of freedom (DoFs) via diamond nitrogen-vacancy (NV) centers in resonators. The gates are heralded by the electron spins associated with the diamond NV centers. In contrast to the ones with one DoF, our implementations reduce the quantum resource and are robust against the decoherence. Evaluations of fidelities and efficiencies of our gates show that our schemes may be implemented with current technology.
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.