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Table 2 Logical qubits necessary in each step in the PRN-type circuit. We neglect registers with only several qubits

From: Quantum pricing with a smile: implementation of local volatility model on quantum computer

Part Register Logical qubit Note
Whole \(R_{\mathrm{samp}}\) \(n_{\mathrm{samp}}\)  
\(R_{S}\) \(n_{\mathrm{dig}}\)  
\(R_{\mathrm{payoff}}\) \(n_{\mathrm{dig}}\)  
\(R_{\mathrm{PRN}}\) \(n_{\mathrm{PRN}}\)  
\(J_{\mathrm{PRN}}\) ancilla \(2n_{\mathrm{PRN}}\) To hold intermediate outputs; see (25)
\(\Phi _{\mathrm{SN}}^{-1}\) \(R_{W}\) \(n_{\mathrm{dig}}\)  
ancilla \(6n_{\mathrm{dig}}\) To hold the coefficients of the polynomial and the intermediate outputs; see Fig. 6
\(V^{(j)}_{k}\) \(R_{W}\) \(n_{\mathrm{dig}}\)  
\(R_{S^{\prime }}\) \(n_{\mathrm{dig}}\)  
ancilla \(4n_{\mathrm{dig}}\) For xx + (ax + b)y and \(z\leftarrow \frac{z+x-by}{1+ay}\); see the comment in the body text.
\(P_{\mathrm{PRN}}\) ancilla \(2n_{\mathrm{PRN}}\) To hold intermediate outputs; see (26).