Table 3 Logical qubits added in each time step in the AE-type circuit. We neglect registers with only several qubits. We only take the leading contributions
From: Quantum pricing with a smile: implementation of local volatility model on quantum computer
Register | Logical qubit | Note | |
|---|---|---|---|
\(R_{S_{i}}\) | \(n_{\mathrm{dig}}\) | ||
\(R_{W_{i}}\) | \(n_{\mathrm{dig}}\) | ||
\(R_{{\mathrm{payoff}},i}\) | \(n_{\mathrm{dig}}\) | ||
\(R_{{\mathrm{LV}},i}\) | \(2n_{\mathrm{dig}}\) | ||
ancilla used for x←x + (ax + b)y in \(U_{t_{i}}\) | \(n_{\mathrm{dig}}\) | See (33) | |
ancilla for \(U^{\mathrm{SN}}_{m},m=1,\dots ,n_{\mathrm{dig}}-1\) | output \(f^{(m)}_{i}\) | \(n_{\mathrm{dig}}^{2}\) | \(n_{\mathrm{dig}}\) for one \(U^{\mathrm{SN}}_{m}\) |
ancilla for SQRT | \(2n_{\mathrm{dig}}^{2}\) | \(2n_{\mathrm{dig}}\) for one \(U^{\mathrm{SN}}_{m}\) | |
qubits used for arccos (input, output and intermediate output) | \(105n_{\mathrm{dig}}\) | 105 for one \(U^{\mathrm{SN}}_{m}\) | |