PHYSICS · Subjective · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · Open quantum systems, decoherence and error correction
Quantum Information and Technology, Ch Order finding and Shor's factoring algorithm
Problem
A popular-science article states: "In 2001, a compiled quantum circuit using 7 nuclear spins factored 15. Since Shor's algorithm's gate count grows only polynomially in L, a machine with roughly 7×(2048/4)≈3600 qubits (scaling the 7 spins by the ratio of bit lengths, 2048 against 15's 4 bits) should be enough to factor a 2048-bit RSA modulus. Because a few thousand qubits is well within reach of current engineering, RSA is close to being broken." Find the errors in this argument.