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A recent article in Quanta Magazine highlights the algorithmic progress in quantum factoring, a field that has excited (and scared) many since Peter Shor's 1994 period-finding algorithm that runs exponentially faster than classical alternatives. Key points include: Challenges in Implementing Shor's Algorithm: Implementing Shor's algorithm is difficult due to the susceptibility of quantum computers to errors. A recent paper estimated that factoring a standard 2,048-bit number would require a quantum computer with 20 million qubits, far beyond the capability of current quantum computers. Oded Regev's Contribution: Oded Regev, a cryptographer, has been exploring the connection between factoring and lattice-based cryptography. He has developed a new approach to quantum factoring by generalizing the periodic function in Shor's algorithm from one dimension to multiple dimensions, leading to a more efficient factoring process. Regev's Algorithm and Its Efficiency: Regev's algorithm reduces the number of logical steps required in the quantum part of the factoring process. This improvement could make the algorithm easier to implement in practice despite the increased number of qubits required. Recent Developments: Following Regev's work, researchers Vaikuntanathan and Ragavan found a way to reduce the memory use of Regev's algorithm, bringing it closer to practical implementation. Regev's work underscores that quantum computing is still open to significant discoveries, even in well-studied areas. It suggests that there may be more efficient quantum algorithms yet to be discovered. https://lnkd.in/gCahZP3C

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