Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity

TL;DR

This paper presents efficient, deterministic, and high-fidelity schemes for implementing controlled-NOT and Fredkin gates in hybrid linear optical systems, reducing resource requirements and achieving high fidelity without ancillary photons.

Contribution

The authors introduce novel linear optical schemes for CNOT and Fredkin gates using hybrid encoding, eliminating the need for ancillary photons and measurement-induced nonlinearities, with simplified optical depths.

Findings

CNOT gate implemented with a single polarization beam splitter

Fredkin gate requires only d PBSs in the generalized scheme

Fredkin gate fidelity exceeds 99.7% under realistic conditions

Abstract

Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom ($d$-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only $d$ PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.