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Optics Letters

Logic-qubit CNOT gates in decoherence-free subspaces assisted by the nitrogen-vacancy center

Li Dong, Zi-Qing Yuan, Zilin Zhao, Si-Ge Chen, Xinyi Zhang, Yan‐Qiang Ji, Jiuming Li, Xiao‐Ming Xiu

Published Dec 12, 2024• 2 citations
Publisher

Abstract

Employing an optical microcavity interacting with a nitrogen-vacancy (NV) center with excellent optical performance and scalability, two logic-qubit controlled-not (CNOT) gates in decoherence-free subspaces (DFSs) are successfully constructed against collective-rotating noise and collective-dephasing noise, respectively. The circuit has a heralded function that can filter out incorrect components. Furthermore, a waveform corrector (WFC) is adopted to balance the amplitude of two components in different spatial modes, thereby achieving high fidelity.

DOI
10.1364/ol.543419

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Employing an optical microcavity interacting with a nitrogen-vacancy (NV) center with excellent optical performance and scalability, two logic-qubit controlled-not (CNOT) gates in decoherence-free subspaces (DFSs) are successfully constructed against collective-rotating noise and collective-dephasing noise, respectively. The circuit has a heralded function that can filter out incorrect components. Furthermore, a waveform corrector (WFC) is adopted to balance the amplitude of two components in different spatial modes, thereby achieving high fidelity.
The implementation of an optical system universal logic-qubit controlled-NOT gate of decoherence-free subspaces (DFSs) using the cross-Kerr nonlinearity effect is discussed. Both the control qubit and the target qubit contain two photons, the states of which are DFSs of collective-rotating noise or collective-dephasing noise. A three-qubit parity-check circuit, which is the most important unit of the quantum gate, is proposed first, and only one ancillary photon is needed in our scheme. A single-photon source, linear optical apparatus, and quantum nondemolition detector are used to perform the process. Its efficiency may approach 100% with a feed-forward process. The experimental feasibility of the strategy with current technology is also considered.
In the paper, we present schemes for implementing multi-qubit quantum gates in quantum networks based on the nitrogen-vacancy (NV) centers in diamond. In our schemes, NV centers coupled to the whispering-gallery modes of microtoroidal resonators serve as quantum registers to store quantum information. By coding the qubits of NV centers into decoherence-free subspaces, quantum information encoded in logical qubits is protected from collective dephasing, and quantum controlled-NOT and Toffoli gates between logical qubits from the same or different quantum nodes can be implemented. Compared with the previous works, our schemes are simpler and reduce the consumption of resources. Furthermore, the modularized design of multi-qubit quantum gates can be extended to other quantum platforms, which may lead to more efficient construction of quantum networks for distributed quantum computation and quantum communication.
High-dimensional quantum systems expand quantum channel capacity and information storage space. By implementing high-dimensional quantum logic gates, the speed of quantum computing can be practically enhanced. We propose a deterministic 4 × 4-dimensional controlled-not (CNOT) gate for a hybrid system without ancillary qudits required, where the spatial and polarization states of a single photon serve as a control qudit of four dimensions, whereas two electron-spin states in nitrogen-vacancy (NV) centers act as a four-dimensional target qudit. As the control qudits are easily operated employing simple optical elements and the target qudits are available for storage, the CNOT gate works in a deterministic way, and it can be flexibly extended to n × n-dimensional (n > 4) quantum gates for other hybrid systems or different photonic degrees of freedoms. The efficiency and fidelity of the CNOT gate are analyzed aligning with current technological capabilities, finding that they have satisfactory performances.
The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.
We present a scheme for implementing robust quantum gates in decoherence-free subspaces (DFSs) with double-dot spin qubits. Through the resonator-assisted interaction, the controllable interqubit couplings can be achieved only by adjusting the qubit transition frequencies. We construct a set of logic gates on the DFS-encoded qubits to eliminate the collective noise effects, and thus the gate fidelities can be enhanced remarkably. This proposal may offer a potential approach to realize the robust quantum computing with spin qubits.
Due to its unique optical properties, nitrogen-vacancy centers in diamond show remarkable advantages in realizing quantum information processing and computation. This paper proposes a scalable quantum computing architecture based on solid-state NV centers. In our scheme, logical qubits are encoded in a decoherence-free subspace (DFS) with Larmor pairs (a pair of the nucleus). And the connection between multiple qubits is assisted by a cantilever probe. Then the high fidelity of the universal quantum gate is achieved by using a series of pulses. Our scheme provides physical feasibility for scalable quantum computing and may pave the way for large-scale quantum computing based on NV centers.