Table 3 Comparing our estimation of \(N_{phy}\) for the RA with³⁰ based on our resource analysis results of required time.

Required time (s)

\(1.40\times 10^6\)

\(2.47\times 10^6\)

\(3.99\times 10^6\)

\(5.37\times 10^6\)

\(2.25\times 10^7\)

\(6.09\times 10^7\)

Number of qubits (proposal)

\(3.52\times 10^6\)

\(4.08\times 10^6\)

\(4.63\times 10^6\)

\(5.81\times 10^6\)

\(8.32\times 10^6\)

\(1.23\times 10^7\)

Number of qubits³⁰

\(3.92\times 10^6\)

\(5.73\times 10^6\)

\(5.95\times 10^6\)

\(5.87\times 10^6\)

\(8.60\times 10^6\)

\(1.92\times 10^6\)