2
$\begingroup$

I am trying to implement the Deutsch algorithm. My steps were:

  1. Write down $|01\rangle$ in a matrix form $A$;
  2. Apply $H^{\oplus2}$ gate to $A$ matrix;
  3. Multiply it with $U_f$ matrix;
  4. Apply $H$ to the first qubit;

After the above steps, I got a matrix:

array([[ 0.        ],
       [ 0.        ],
       [-0.70710678],
       [ 0.70710678]])

How should I perform a measurent step on the first qubit to get the answer?

$\endgroup$
  • $\begingroup$ What basis is the vector in? $\endgroup$ – Yuval Filmus Mar 1 '19 at 21:52
  • $\begingroup$ Basis vectors are {1,0} and {0,1} $\endgroup$ – Kenenbek Arzymatov Mar 1 '19 at 22:41
2
$\begingroup$

You haven’t specified the order of entries in your vector. In general, the $i$’th entry is obtained with probability $|x_i|^2$.

Let’s consider two examples. In the first, the order of entries is $|00\rangle, |01\rangle, |10\rangle, |11\rangle$. The two final entries will be obtained with probability $1/2$ each, and so the first qubit will be measured as $|1\rangle$. If you measure only the first qubit, then you will still always get $|1\rangle$, and the other qubit will remain in the superposition $\frac{1}{\sqrt{2}}(|1\rangle-|0\rangle)$.

If the order of entries is instead $|00\rangle, |10\rangle, |01\rangle, |11\rangle$, then once again the two final entries will be obtained with probability $1/2$ each. This means that the first qubit will be measured as $|0\rangle$ or $|1\rangle$ with equal probability.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.