Loss-tolerant cross-Kerr enhancement via modulated squeezing

We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single mode, the cross-Kerr interaction strength can be generically amplified. We generalize the result to multi-mode cross-Kerr interactions and show that single-mode squeezing can be used to achieve a cross-Kerr enhancement that increases exponentially in the number of modes involved. As one application of the proposed protocol, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and demonstrate that the protocol can overcome photon losses. Finally, we discuss experimental realizations of the scheme in optical fibers and nanophotonic waveguides.