# Simulating Measurement in Python

In this lesson, we look at measuring qubits and reading the results of our quantum computations.

## We'll cover the following

In this chapter, we started by creating quantum states and gates in **NumPy**. We then put those together and saw how one could apply gates to single and multi-qubit systems. Finally, in this lesson, we shall complete this computation puzzle and measure the state of our quantum system.

## Measurement under the hood

Recall that measurement takes qubits to the computational basis states $|0\rangle$ and $|1\rangle$. Intuitively, this meant that we were transferring information of the qubit state in a classical register whose value we could read. Mathematically, this process is defined as taking the **inner product** of an arbitrary state $|\phi\rangle$ with the conjugate transpose of the $|x\rangle$, which is the state we want to measure $|\psi\rangle$ in:

$p(|x\rangle)=|\langle x|\phi\rangle|^2$

This operation is easily implemented in **NumPy**. The code below shows the probability of measuring state $|\phi\rangle=\frac{1}{\sqrt{2}}|0\rangle-\frac{i}{\sqrt{2}}|1\rangle$ in the state $|1\rangle$.

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