(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I've pasted the actual question below:

http://www.zeta-psi.com/aj/qip5b.png [Broken]

I don't think there are many quantum computing specific things here other than the circuit (which I can derive easily if I can figure out the algorithm)

2. Relevant equations

The Quantum Fourier Transform: http://en.wikipedia.org/wiki/Quantum_fourier_transform" [Broken]

Helpful Identities:

http://en.wikipedia.org/wiki/Euler%27s_formula_in_complex_analysis" [Broken]

[tex]M=\sum_i m_i P_i[/tex], I'm assuming [tex]P_i^n = P_i[/tex] where [tex]n >= 1[/tex] is.

Also, I'm assuming that [tex]M^2 \neq I[/tex], in that case Icouldhave used the identity [tex]e^{iAx} = cos(x)I + isin(x)A[/tex] but I can't.

3. The attempt at a solution

I've tried letting [tex]|x> = \sum_{i=0}^{N-1} |i>[/tex], then from there, I can perform an inverse QFT on [tex]|x>U^x|\psi_j>[/tex] where [tex]|\psi_j>[/tex] is some eigenvalue of [tex]U[/tex] (and thus also [tex]U^x[/tex]) to get me [tex]|\omega>[/tex] which Icoulduse in replacement of M in the definition of U.

Assuming I'm not making a trivial mistake, I'm assuming the observable itself I want to find is [tex]M|\psi_j>[/tex], which I can then use to find [tex]M|\psi>[/tex] (since spectral decomposition lets me write this as the sum of eigenvectors).

I think the key somehow revolves around writing the eigenvalues of [tex]M|\psi_j>[/tex] in terms of the eigenvalues of U for each [tex]|\psi>[/tex], assuming that they even have the same eigenvector bases.

I've also tried expanding [tex]e^{2\pi i M/N}[/tex] and I was able to (partially) factor out the [tex]M[/tex], but I wasn't sure where to go from there.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Hint for Quantum Computing Question Regarding QFT's and Eigenvalue Estimation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**