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Explore an innovative quantum factoring algorithm presented by Oded Regev from NYU in this 1 hour 53 minute Quantum Colloquium talk. Delve into the details of a method that can factorize n-bit integers using a quantum circuit with \tilde{O}(n^{3/2}) gates, run \sqrt{n}+4 times independently, followed by classical post-processing. Compare this approach to Shor's algorithm, which requires circuits with \tilde{O}(n^2) gates. Understand the number-theoretic heuristic assumption underlying the algorithm's correctness, similar to those used in subexponential classical factorization algorithms. Consider the potential implications and limitations of this method for practical physical implementations. The talk includes a panel discussion starting at 1:08:21, providing further insights and perspectives on this cutting-edge research in quantum computing and cryptography.
