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 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.
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.
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.
Compared with traditional two-dimensional qubits, higher-dimensional qubits offer a larger state space for storing and processing information, which can manifest stronger non-classical correlations, simplify circuit complexity, reduce computational resources, and enhance loss tolerance in photon-based quantum information processing. To harness the potential, essential research on preparing qudit-based high-dimensional entangled states is necessary. In the paper, we propose the preparation procedure of arbitrary four-dimensional two-qudit entanglement and three-qudit entanglement for photon systems implemented with error-heralded quantum devices and controlled-not gates. Moreover, as the practical errors that grow out of defective photon scattering, i.e., coupling strength restriction of the quantum-dot-cavity system and cavity leakage imperfection, can be turned into the response of the single-photon detectors, the generation of arbitrary high-dimensional entanglement appears in an error-heralded way, and their fidelities are robust, enhancing experimental accessibility.
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.
Qudit, a high-dimensional quantum system, can provide a larger Hilbert space, and it has been shown that the larger Hilbert space has remarkable advantages over the smaller one in quantum information processing. However, it is a great challenge to realize the high-fidelity quantum gates with qudits. Here we theoretically propose and experimentally demonstrate the four-dimensional quantum gates (including the generalized Pauli X4 gate, Pauli Z4 gate, and all of their integer powers) with optical qudits based on the polarization-spatial degree of freedom of the single photon. Furthermore, we also realize the polarization-controlled eight-dimensional controlled-X4 gate and all of its integer powers. The experimental results achieve both the ultrahigh average gate fidelity 99.73 and efficiency 99.47, which are above the error threshold for fault-tolerant quantum computation. Our work paves the way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.
High-dimensional quantum gates not only extend the existing quantum computing framework but also serve as a vital component in a range of quantum technologies. In the study, a 4 × 4-dimensional controlled-NOT (CNOT) gate is presented based on the assistance of a weak cross-Kerr medium, utilizing only two degrees of freedom (DoFs) with two photons. Specifically, the control qudits are encoded in the photonic polarization DoF, while the target qudits are encoded in the path DoF of the two photons. Notably, the circuit is constructed using only two times of the Kerr medium, outperforming a previous design that required six times, which simplifies the entire circuits. Furthermore, the fidelity and success probability of the proposed protocol are near 1 when the influence factors take the appropriate value.