Abstract The high‐dimensional Toffoli gate functions in a broader Hilbert space, which empowers it to convey and handle greater amounts of information through parallel quantum pathways. In this study, a scheme of 3‐qudit ‐D Toffoli gate in the QD cavity‐coupling system with high fidelity is proposed. By modulating Purcell factor, the balanced condition is obtained so that the error induced by whether there is interaction between the QDs and cavities or not can be neglected. The scheme features a module circuit design, which not only ensures higher construction feasibility but also helps save resources. Meanwhile, it possesses technical scalability, enabling effective promotion to the application scenarios of n ‐qudit systems, which reduces the steps required to manipulate quantum states and makes it simpler to construct quantum computing circuits.
Abstract The high‐dimensional Toffoli gate functions in a broader Hilbert space, which empowers it to convey and handle greater amounts of information through parallel quantum pathways. In this study, a scheme of 3‐qudit ‐D Toffoli gate in the QD cavity‐coupling system with high fidelity is proposed. By modulating Purcell factor, the balanced condition is obtained so that the error induced by whether there is interaction between the QDs and cavities or not can be neglected. The scheme features a module circuit design, which not only ensures higher construction feasibility but also helps save resources. Meanwhile, it possesses technical scalability, enabling effective promotion to the application scenarios of n ‐qudit systems, which reduces the steps required to manipulate quantum states and makes it simpler to construct quantum computing circuits.
Abstract A high‐dimensional quantum gate not only enables the processing of more information through parallel quantum channels but also enhances fault tolerance in a higher Hilbert space. In this paper, a protocol is presented for implementing a three‐qudit ‐Dimensional (D) Toffoli gate for a hybrid system, where the first control qudit, the second control qudit, and the target qudit of four dimension are encoded in the spatial‐polarization state of a flying photon, the electron‐spin state of the first two quantum dots (QDs), and the one of the remaining two QDs, respectively. Besides, the high‐dimensional Toffoli gate does not require any assistance. Moreover, the gate operates deterministically in principle, as the photon is easy to manipulate feasibly using simple optical elements, and four QDs have a long electron‐spin coherent time used for storage and manipulation. Furthermore, the success probability and fidelity of the high‐dimensional Toffoli gate, in alignment with current technological capabilities, demonstrate satisfactory results. This indicates that it is feasible in experimental settings and promises a quantum computing paradigm that excels in speed, error resilience, and scalability for intricate quantum operations.
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.
Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a 4 × 4 -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a 4 × 4 × 4 -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV−) center, resulting in saving resources. Moreover, since the imperfect NV−-cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.
Abstract Quantum computation in high‐dimensional (HD) spaces holds significant promise for advancing a broad range of applications within quantum information technology (QIT), leading to processing more complex information and executing a wider array of quantum operations. In this study, a measurement‐free auxiliary cavity‐atom system is exploited to construct a three‐qudit photonic Toffoli gate in a ‐dimensional space. In addition, the auxiliary system maintains its initial state after a series of operations, eliminating the need for measurement and facilitating effective interactions between different photons by leveraging its extended coherence time. A comprehensive analysis of its fidelity and efficiency is performed, yielding impressive results that demonstrate the superiority and flexibility of this proposed protocol. Furthermore, the HD Toffoli gate lays the groundwork for realizing HD quantum computation for photon systems and significantly improves the efficiency of QIT.
Realizing high-fidelity n-qubit quantum controlled-not gates is of critical significance. Applying quantum-dot (QD) spins as qubits, an (n - 1)-qubit control 1-qubit not gate and a 1-qubit control (n - 1)-qubit not gate is constructed. By utilizing the balanced condition, even under the condition of weak coupling, the circuit including the wave-form correctors and the balanced reflection condition of the cavity may effectively reduce the noise resulting from the unequal reflectance, so that the fidelity of each quantum gate operation can be increased to unity in theory. The operational complexity is further reduced, considering that low-Q cavities are used. In addition, the control gate of m-qubit control (n - m)-qubit can also be performed with a similar device diagram, only by changing the numbers of the control qubits and target qubits. These n-qubit controlled-not gates can help construct simpler quantum computing circuits that can be widely applied in quantum information processing.
High-fidelity quantum logic gates are essential in quantum computation, and both photons and electron spins in quantum dots (QDs) have their own unique advantages in implementing quantum computation. It is of critical significance to achieve high-fidelity quantum gates for photon-QD hybrid systems. Here, we propose two schemes for implementing high-fidelity universal quantum gates including Toffoli gate and Fredkin gate for photon-QD hybrid systems, utilizing the practical scattering of a single photon off a QD-cavity system. The computation errors from the imperfections involved in the practical scattering are detected and prevented from arising in the final results of the two gates. Accordingly, the unity fidelity of each quantum gate is obtained in the nearly realistic condition, and the requirement for experimental realization is relaxed. Furthermore, the quantum circuits for the two gates are compact and no auxiliary qubits are required, which would also be the advantages regarding their experimental feasibility. These features indicate that our schemes may be useful in the practical quantum computation tasks.