A Computation-Strengthened High-Dimensional Three-Qudit Toffoli Gate

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 $4\times 4\times 4$-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.