Lower bound for quantum phase estimation
Abstract
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower-bound approaches to the case where the oracle Q is given by controlled powers Qp of Q , as it is, for example, in Shor’s order-finding algorithm. In this setting we will prove a Ω(log1/γ) lower bound for the number of applications of Qp1 , Qp2,… . This bound is tight due to a matching upper bound. We obtain the lower bound using a technique based on frequency analysis.
- Publication:
-
Physical Review A
- Pub Date:
- April 2005
- DOI:
- 10.1103/PhysRevA.71.042313
- arXiv:
- arXiv:quant-ph/0412008
- Bibcode:
- 2005PhRvA..71d2313B
- Keywords:
-
- 03.67.Lx;
- Quantum computation;
- Quantum Physics
- E-Print:
- 7 pages, 1 figure