Improved Entanglement-Based High-Dimensional Optical Quantum Computation with Linear Optics

Quantum gates are the essential block for quantum computers. High-dimensional quantum gates exhibit remarkable advantages over their 2D counterparts for some quantum information processing tasks. Here, a family of entanglement-based optical controlled-SWAP gates on C-2 circle times C-d circle times C-d is presented. With the hybrid encoding, the control qubits and target qudits are encoded in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only (2+3d) (d >= 2) linear optics, beating an earlier result of 14 linear optics with d=2. The circuit depth five is much lower than an earlier result of 11 with d=2. Besides, the fidelity of the presented circuit can reach 99.4%, and it is higher than the previous counterpart with d=2. The scheme is constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Moreover, the approach allows d>2.