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 x←x + (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). |