I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation.
 Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution starts from the ground state of $H_B$ and slowly evolves until it arrives at the ground state of $H_P$. In section 3.1, the one qubit example has the adiabatic Hamiltonian as $$\tilde{H}(s) = \begin{pmatrix}
s &amp; \epsilon (1-s) \\ 
\epsilon (1-s) &amp; 1-s   
\end{pmatrix}$$
I don't see how the plot of Figure 1 is drawn. In figure 1, Farhi plotted eigenvalues of the Hamiltonian for s while the range for s was 0 to 1. The Hamiltonian is supposed to evolve according to the Schrodinger equation (eq 2.1), $$i \frac{d}{dt} |\Psi (t) \rangle = H(t) |\Psi (t) \rangle$$
Was this evolution solved to draw the plot? Or did Farhi derive the formula for eigenvalues in terms of s using just matrix math and plotted accordingly?


Question: ASP.net Website want debug to == false on IIS
Answer: compilation debug element is not the same thing as DEBUG preprocessor directive.
You need to re-compile your website in Release mode.


  What about binaries compiled with debug symbols?
  
  One scenario that several people find very useful is to
  compile/pre-compile an application or associated class libraries with
  debug symbols so that more detailed stack trace and line error
  messages can be retrieved from it when errors occur. 
  
  The good news is that you can do this without having the have the
   switch enabled in production. 
  Specifically, you can use either a web deployment project or a web
  application project to pre-compile the code for your site with debug
  symbols, and then change the  switch to
  false right before you deploy the application on the server. 
  
  The debug symbols and metadata in the compiled assemblies will
  increase the memory footprint of the application, but this can
  sometimes be an ok trade-off for more detailed error messages.


http://weblogs.asp.net/scottgu/archive/2006/04/11/Don_1920_t-run-production-ASP.NET-Applications-with-debug_3D001D20_true_1D20_-enabled.aspx