Efficient factorization with a single pure qubit and $log N$ mixed qubits — mentioned by Strilanc

Tue, 11 Apr 2023 16:23:14 GMT

> Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase [..] to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation. This is wrong. Those rotations are not the hard part. When Shor's algorithm is compiled using qubit recycling [0], factoring an n bit number uses 2n rotations that aren't a multiple of 45 degrees. For relevant number-to-factor sizes like 2048 bits, performing these rotations to a precision of ±0.0000000001° is more than sufficient. Rotations smaller…

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Efficient factorization with a single pure qubit and $log N$ mixed qubits · HackerPapers discussions

Efficient factorization with a single pure qubit and $log N$ mixed qubits — mentioned by Strilanc