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.
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.
Abstract Enhancing the capabilities of quantum computing relies heavily on harnessing the power of qudit‐based high‐dimensional quantum gates. In the study, single‐qudit 4D , , and gates tailored for a two‐photon system in polarization states are presented. Furthermore, a two‐qudit ‐dimensional controlled‐not (CNOT) gate designed for a four‐photon system is introduced. These high‐dimensional gates can offer versatile and straightforward optical implementations, ensuring them to fulfill in a deterministic way. To facilitate these processes, an auxiliary system in the form of a ‐type atom residing in a cavity is employed. Remarkably, the auxiliary system retains its original state after the operation process ends, so it is not required to measure and plays a pivotal role in promoting effective interactions among distinct photons in its extended coherence time. Importantly, the in‐depth analysis of the fidelities and efficiencies of these quantum gates showcase remarkable outcomes, affirming the superiority of the proposed protocols. Therefore, these high‐dimensional gates not only amplify quantum parallelism, but also bolster the speed of quantum computations, fortify resilience against errors, and foster scalability for executing intricate quantum operations.
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 High‐efficiency quantum information processing is equivalent to the fewest quantum resources and simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three‐level Λ‐type atom‐cavity system, the authors present some refined protocols for realizing controlled‐not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of gates is encoded on a flying photon, and the remaining qubits are encoded on the atoms in the optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi‐qubit CNOT, Fredkin, and Toffoli gates with optical elements without auxiliary photons or atoms. Further, the simplest single‐qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.
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 gates designed with minimized resources overhead have a crucial role in quantum information processing. Here, based on the degrees of freedom (DoFs) of photons and Λ‐type atom systems, two high‐fidelity and low‐cost protocols are presented for realizing polarization‐spatial hyperparallel controlled‐not (CNOT) and Toffoli gates on photon systems with only two and four two‐qubit polarization–polarization swap (P‐P‐SWAP) gates in each DoF, respectively. Moreover, the quantum gates can be extended feasibly to construct 2m‐target‐qubit hyperparallel CNOT and 2n‐control‐qubit Toffoli gates required only 4m and 4n P‐P‐SWAP gates on ‐ and ‐photon systems, respectively, which dramatically lower the costs and bridge the divide between the theoretical lower bounds and the current optimal syntheses for the photonic quantum computing. Further, the unique auxiliary atom of these quantum gates can be regarded as a temporary quantum memory that requires no initialization and measurement, and is reused within the coherence time, as the state of the atom remains unchanged after the hyperparallel quantum computing.
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.