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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 xx + (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 \(U^{\mathrm{SN}}_{m}\)