Mixed quantization

Zhou Qing Ping

We show that Wu-Yang theory of fully quantized four-wave mixing can be generalized to the six-wave mixing and derive the analytical solution of the coupled equations describing the quantum dynamics of six-wave mixing.

Heimo G. Latal, W. Schweiger

Cing-Yuan Lai, Chin-Fu Nien, Lien-Po Yu +1 more

Mixed-precision quantization (MPQ) aims to assign different bit-widths to different neural network layers, balancing accuracy and efficiency. Prior studies have formulated the MPQ search problem as an integer linear programming (ILP) prob-lem, relying on layer-wise importance indicators derived from quantization-aware training. This work proposes an alternative approach that reformulates the MPQ as a Quadratic Uncon-strained Binary Optimization (QUBO) problem, which can be solved effectively using the quantum-inspired annealers. This method leverages learned importance indicators while enabling flexible incorporation of additional constraints via soft penalty terms. Experimental results on the Imagenette dataset demon-strate that our QUBO-based approach achieves quantization policies with comparable performance to the ILP-based method, validating its effectiveness.

Gerald V. Dunne

Holger Schanz, Bernd Esser

The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.