0

enter image description here

where

enter image description here

How can we prove these two quantum oracles are equivalent: $$O_x:|x,b\rangle\mapsto|x,b\oplus f(x)\rangle$$ and $$O_z:|x⟩ \mapsto(−1)^{f(x)}|x⟩$$

venki
  • 1
  • 1
  • They're not based on the information you provided. I feel like there's some missing context here. – Dani007 Nov 28 '22 at 13:06

1 Answers1

1

The two oracles are not equivalent. But if you have either one of these oracles, you can trivially construct the other. In that sense they are equivalent.

Converting a phase oracle into a standard oracle is discussed here.

To convert a standard oracle into a phase oracle is discussed in the Wikipedia article on Grover's Algorithm. Put $|-\rangle$ into the "result" qubit before running the algorithm.

Frank Yellin
  • 713
  • 2
  • 8
  • Thank you very much for your reply! – venki Nov 28 '22 at 22:02
  • @venki If the answer helped you/solved your problem, please remember to upvote it and mark it as accepted! :) – Tristan Nemoz Nov 29 '22 at 00:46
  • Surely conversion from phase into standard only works of you've got a controlled version of the phase oracle? So if you've only got the non-controlled version, that doesn't help with an equivalence claim? – DaftWullie Nov 29 '22 at 16:36