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In excellent agreement with our numerical simulations of Shor's algorithm, equipped with a truncated quantum Fourier transform of bandwidth b, we find that its performance scales ∼2 −ξ b n , where n is the number of qubits, ξ b = 1.1 × 2 −2b , and the bandwidth b is the number of quantum states coupled by the quantum Fourier transform. Nonexponential behavior is observed for small n and explained analytically. The large-n exponential scaling implies that b = 7 is sufficient to operate adoi:10.1103/physreva.86.044303 fatcat:4j3pmd5bunhxtf5out24miquyy