Applications of Spin-Dependent Generalized Squeezing in Hybrid Spin-Oscillator Quantum Processors
Generalized squeezing interactions are foundational to quantum optics, and have recently come under experimental control in hybrid spin-oscillator quantum processors [O. B\u{a}z\u{a}van, et al., Nat. Phys. 22, 757 (2026); S. Saner, et al., Phys. Rev. X 16, 021049 (2026)]. These interactions open the door for new applications in the processing of discrete- and continuous-variable quantum information, four of which we propose and investigate in this work: geometric phase gates mediated by spin-dependent generalized squeezing acting on two spins and a common oscillator; genuine N-body spin interactions mediated by individually addressed spin-dependent generalized squeezing; oscillator thermometry via spin readout; and the preparation of high-fidelity quantum states of the oscillator via spin-dependent generalized squeezing and mid-circuit measurement. A unifying feature of these applications is the geometric phase induced by generalized squeezing interactions, which is nonlinear in the Fock occupation of the oscillator and the interaction order of the generalized squeezing. This work provides a foundation for fast, high-fidelity discrete- and continuous-variable quantum computation and sensing in the hybrid spin-oscillator platform via generalized squeezing.