Deterministic preparation of squeezed and non-Gaussian states in coupled qubit-boson systems

Abstract

Deterministic preparation of bosonic resource states is a central task in continuous-variable quantum information processing and quantum metrology. Here we develop a measurement-based imaginary time evolution (MITE) protocol for preparing squeezed and non-Gaussian states. The protocol combines ancilla-mediated weak measurements of the Hamiltonian with a conditional phase rotation that suppresses excited state trapping and stabilizes convergence toward the ground state. The method is potentially applicable in hybrid discrete variable-continuous variable (DV-CV) platforms, where the qubit acts as the measurement readout. We demonstrate deterministic convergence over a broad range of parameters and show that the performance degradation near the stability boundary is governed by the shrinking Bogoliubov quasiparticle gap. The same framework also extends to non-Gaussian bosonic resource states, including Schr\"odinger cat states and excited states of the single-mode squeezing Hamiltonian, which display Wigner negativity. The squeezed states remain robust under bosonic loss over experimentally relevant regimes.