Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.
For each choice of the four bitstrings satisfyingm⊕n⊕p⊕q=0, the distinct values ofxthat give a non-zero contribution arex=0,x=m⊕n,x=m⊕p, andx=m⊕q
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The true cost of factoring: Linking magic and number-theoretic complexity in Shor's algorithm
Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.