Is the QFT physically realizable for modest qubits?
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I’m not an expert in quantum computing. I’m just an electrical engineer who’s interested in quantum computing because of its implications for encryption. Shor’s algorithm can break RSA encryption in polynomial complexity. The algorithm relies on a quantum Fourier transform in n qubits where n is the number of classical bits of the semiprime that you’re trying to factor. From what I’ve read just on Wikipedia, the QFT requires a phase gate with π/2^n phase change. I may be missing something, but I don’t really understand how a practical phase gate with the required precision for modern encryption could ever be implemented. Modern RSA typically uses 4096 bit modulus. What physical system could create a phase change with 4096-bit precision? That’s more than 1000 orders of magnitude. That’s larger than ratio of the size of the observable universe to the Planck length. It’s larger than the ratio of the age of the observable universe to Planck time. Is there a workaround to using such precise phase gates? Even a modest number of qubits (more than 40) doesn’t seem realizable for QFT. submitted by /u/DiscretePoop [link] [comments]