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 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 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.
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.
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 Qudit‐based quantum gates offer several advantages over qubit‐based counterparts, such as higher information density, the ability to address more complex problems, and richer quantum operations. In this study, three realistic protocols are presented for implementing a 44‐dimensional (16D) two‐qudit controlled‐SUM (CSUM) gate, where the 4D control qudit and 4D target qudit are encoded in the polarization degree of freedom (DoF) and spatial DoF of two photons, respectively. The first protocol is implemented exclusively using linear optical elements without auxiliary resources, making it feasible with current optical technologies and achieving an efficiency of 1/9. The second protocol utilizes photon scattering by a microcavity‐quantum‐dot system, enabling the 16D CSUM gate to operate deterministically without postselection. The third protocol introduces an error‐heralded mechanism based on the second protocol, theoretically achieving unity fidelity. Moreover, all protocols operate without ancillary photons, offering the advantages of compact circuits and low cost while further promoting the development of high‐dimensional quantum computation.
Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.
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.