Fig. 4: Contrasting Shor’s circuit with an idealized hybrid circuit \({{{{\mathcal{Q}}}}}_{a,N}^{\rm ideal}\). | Nature Communications

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

Fig. 4

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.

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