Quantum Fourier transform
A QC can compute a FT in one step (see Chuang handout)
- Fourier transform is reversible
- Define a Fourier operator UFT.
- Example: Take UFT?000?
UFT?000? = {?000? + ?001? +?010? +?011? +?100? +?101? +?110? +?111?}
How do we read the output?
- If we measure the output, it collapses into a base state…
- We can run the UFT exponentially many times, to accumulate output statistics
- Or we can be very clever…
- See pgs. 21-24 of the Chuang handout: Deutsch’s problem