Linear-optical implementations of the iSWAP and controlled NOT gates based on conventional detectors

Abstract

The majority of linear-optical nondestructive implementations of universal quantum gates are based on single-photon resolving detectors. We propose two implementations, which are nondestructive (i.e., destroying only ancilla states) and work with conventional detectors (i.e., those which do not resolve a number of photons). Moreover, we analyze a recently proposed scheme of Wang [J. Opt. Soc. Am. B27, 27 (2010)] of an optical iSWAP gate based on two ancillae in Bell’s states, classical feedforward, and conventional detectors with the total probability of success equal to η4/32, where η is detector’s efficiency. By observing that the iSWAP gate can be replaced with the controlled NOT gate with additional deterministic gates, we list various possible linear-optical implementations of the iSWAP gate: (i) assuming various ancilla states (unentangled, two-photon, and multiphoton-entangled states) or no ancillae at all, (ii) with or without classical feedforward, (iii) destructive or nondestructive schemes, and (iv) using conventional or single-photon detectors. In particular, we show how the nondestructive iSWAP gate can be implemented with the success probability of η4/8 assuming the same ancillae, classical feedforward, and a fewer number of conventional detectors than those in the scheme of Wang et al. We discuss other schemes of the nondestructive universal gates using conventional detectors and entangled ancillae in a cluster state, and Greenberger–Horne–Zeilinger and Bell’s states giving the success probabilities of η4/4, η6/8, and η4/8, respectively. In the latter scheme, we analyze how detector imperfections (dark counts in addition to finite efficiency and no photon-number resolution) and imperfect sources of ancilla states deteriorate the quantum gate operation.