Linear optical quantum computing with photonic qubits

TLDR

Linear optics with photon counting is a prominent candidate for practical quantum computing, and the Knill–Laflamme–Milburn protocol demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible, with subsequent improvements bridging the gap between theoretical scalability and practical implementation. The authors review the original theory and its improvements and provide examples of experimental two‑qubit gates. They discuss the use of realistic components, the errors they induce, and how these errors can be corrected.

Abstract

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. We review the original theory and its improvements, and we give a few examples of experimental two-qubit gates. We discuss the use of realistic components, the errors they induce in the computation, and how these errors can be corrected.