Generic Two-Qubit Photonic Gates Implemented by Number-Resolving Photodetection

TL;DR

This paper presents optimized linear-optical implementations of two-qubit entangling gates using number-resolving photodetection, achieving higher success probabilities and reduced resource overhead compared to traditional methods.

Contribution

It introduces a numerical optimization approach combined with symmetry considerations to implement generic two-qubit gates with improved success rates and fewer ancilla photons.

Findings

Controlled-U gates can be implemented with success probability > 0.05 using two ancillas.

A generic SU(4) gate requires three unentangled ancillas with success > 0.0063.

Single-shot implementation of SU(4) gates significantly increases success probability and reduces resources.

Abstract

We combine numerical optimization techniques [Uskov et al., Phys. Rev. A 79, 042326 (2009)] with symmetries of the Weyl chamber to obtain optimal implementations of generic linear-optical KLM-type two-qubit entangling gates. We find that while any two-qubit controlled-U gate, including CNOT and CS, can be implemented using only two ancilla resources with success probability S > 0.05, a generic SU(4) operation requires three unentangled ancilla photons, with success S > 0.0063. Specifically, we obtain a maximal success probability close to 0.0072 for the B gate. We show that single-shot implementation of a generic SU(4) gate offers more than an order of magnitude increase in the success probability and two-fold reduction in overhead ancilla resources compared to standard triple-CNOT and double-B gate decompositions.