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. Dans ce document, we present
three realistic protocols for implementing a 4$\times$4-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.

Cet article explore les excursions dans le temps et leurs implications.

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