A Practical Guide To Quantum Amplitude Amplification

Hands-On Quantum Machine Learning With Python

The last week was exciting. Last Tuesday, my Kickstarter Campaign on Hands-On Quantum Machine Learning With Python started! On Wednesday, it was completely funded already. Thank you so much for your support!

After all this excitement, it’s time to get done some work, again. Today, we learn how Grover’s search algorithm works for two qubits.

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Grover’s search algorithm is one of the first and most prominent examples to show how a quantum circuit can be magnitudes faster than a classical algorithm

In a previous post, we built a conceptual understanding of how the algorithm works. It follows a simple procedure. A quantum oracle inverts the amplitude of the searched state. Then, the diffuser flips all states about the mean amplitude, therefore, magnifying the searched state.

We learned that we can use phases to amplify an amplitude. If we apply an HZH-sequence, it turns a qubit from state |0⟩ into state |1⟩.

But an HIH-sequence turns a qubit from |0⟩ into |+⟩ and back into |0⟩.

While the start and the end of the circuit remain unchanged, we can control the final amplitude of a qubit by its phase that we either flip (HZH) or not (HIH)

In a single-qubit circuit, these circuit identities seem rather be trivial.

In today’s post, we look at how we can employ them practically with two qubits and four states.

My Kickstarter campaign is still live. Don’t miss your chance to get a copy of Hands-On Quantum Machine Learning With Python