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In this paper,May and Schlieper claim that one can find the period of a function $f()$ by embedding $h \circ f = h(f(x))$ for input $x$. This would have the immediate consequence of reducing the number of output qubits. What's more, they say that even a one bit hash function would be enough to run Shor's algorithm and get reasonably good results. This is at a price of performance.

My questions are, how reasonable are these claims? What is the impact on post quantum RSA security? Post quantum RSA security is considered by some people as not that worrisome since it requires a non negligible number of qubits to be practically broken.

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