HW1 - Problem 4
Problem 4
Consider the following 3 qubit state.
\(\left|\phi\right> = \frac{\sqrt{3}}{4}\left|000\right> + \frac{1}{4}\left|001\right> + \frac{1}{2\sqrt{2}}\left|010\right> + \frac{1}{2\sqrt{2}}\left|011\right> + \frac{1}{4}\left|100\right> + \frac{\sqrt{3}}{4}\left|101\right> + \frac{1}{2\sqrt{2}}\left|110\right> + \frac{1}{2\sqrt{2}}\left|111\right>\)
- Suppose we measure all three qubits. What is the probability that we see \(\left|000\right>\)? What is the state of the system after the measurement?
- Suppose instead we only measure the first qubit, and get the result \(\left|1\right>\). What is the probability of this occurring? What is the state after the measurement?
Write the full matrix result of the tensor product, and how each one would transform the following state:
\(\left|\psi\right> := \frac{1}{\sqrt{2}} \left|01\right> + \frac{1}{\sqrt{2}} \left|10\right>.\)
- \(X \otimes I\)
- \(I \otimes Z\)
- \(X \otimes Z\)
- What is the result of the following circuit?
- What is the result of the following circuit?
- If we had \(n\) qubits and applied a Hadamard gate to each of them, what is the resulting state?