Amplification of bosonic interactions through modulated squeezing in the presence of noise and photon losses

We show that bosonic interactions described by a certain class of quadratic and quartic Hamiltonians can be enhanced through a squeezing protocol that can overcome noise and photon losses. The method applies squeezing operations in alternating directions to the modes of interest, which results in a generic amplification of both desired and undesired interactions present in the system. We show that depending on the case, detrimental processes can be less amplified than the desired couplings. We leverage this observation to improve the fidelity for preparing a maximally entangled state by means of unitary dynamics under the simultaneous action of different decoherence mechanisms. Additionally, we investigate noise models in which the protocol either fails or partially achieves a loss-tolerant state preparation speedup. Our work facilitates the preparation of complex quantum states and the implementation of entangling gates in the presence of photon losses and noise.