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Shor's algorithm with fewer (pure) qubits

Christof Zalka
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Abstract

In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which none of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements later on). Then I show how the modular additions in the algorithm can be carried out with a superposition of an arithmetic sequence. This makes parallelisation of Shor's algorithm easier. Finally I show how one can factor with only about 1.5n qubits, and maybe even fewer.

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Christof Zalka. 2006-01-15. Shor's algorithm with fewer (pure) qubits. https://arxiv.org/abs/quant-ph/0601097

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