Fig. 4: Contrasting Shor’s circuit with an idealized hybrid circuit \({{{{\mathcal{Q}}}}}_{a,N}^{\rm ideal}\).
From: Factoring an integer with three oscillators and a qubit

Instead of modular exponentiation followed by Fourier transform and computational-basis measurement in Shor’s circuit (a), our idealized hybrid circuit \({{{{\mathcal{Q}}}}}_{a,N}^{\rm ideal}\) (b) employs standard (real) exponentiation and homodyne detection; modularity (i.e., realizing \(\,({{{\rm{mod}}}}\,\,N)\) computations) is recovered by initializing the second bosonic mode in a modified GKP state with spacing N.