Skip to main content

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


Logical qubit














ancilla used for xx + (ax + b)y in \(U_{t_{i}}\)


See (33)

ancilla for \(U^{\mathrm{SN}}_{m},m=1,\dots ,n_{\mathrm{dig}}-1\)

output \(f^{(m)}_{i}\)


\(n_{\mathrm{dig}}\) for one \(U^{\mathrm{SN}}_{m}\)

ancilla for SQRT


\(2n_{\mathrm{dig}}\) for one \(U^{\mathrm{SN}}_{m}\)

qubits used for arccos (input, output and intermediate output)


105 for one \(U^{\mathrm{SN}}_{m}\)