Fig. 3: The physically realizable quantum circuit \({{{{\mathcal{Q}}}}}_{a,N}\), where \(a\in {{\mathbb{Z}}}_{N}^{*}\).
From: Factoring an integer with three oscillators and a qubit
See Supplementary Table 1 for a suitable choice of parameters R, m, ΔA, κA, ΔB, κB, ΔC. It applies a sequence of elementary operations and derived unitaries (see Figs. 1, 2) to two approximate GKP states in the first and second mode, a vacuum state \(\left|{\mathsf{vac}}\right\rangle\) in the third mode and a qubit computational basis state \(\left|0\right\rangle\) in the qubit system. The output is a sample \(w\in {\mathbb{R}}\) obtained by performing a P-quadrature measurement on the first mode. The shaded subcircuit approximately computes a pseudomodular power. To provide intuition, we will first discuss the effect of the circuit when this subcircuit is replaced by an ideal unitary \({U}_{{\mathbb{R}},a,N}^{{{{\rm{ideal}}}}}\) computing the real power, see Fig. 4b.
