The Hamiltonian — A quantum machine learning story

But the name-giver had nothing to do with quantum mechanics

Do you want to get started with Quantum Machine Learning? Have a look at Hands-On Quantum Machine Learning With Python.

The Hamiltonian is a quantum operator that describes the possible energies of a physical system. Doesn’t it sound like a big deal? But it is. Because if we know the Hamiltonian, we can calculate the system's behavior.

You already know some quantum operators. They transform the qubit state. For example, the 𝑋 gate flips the amplitudes of states |0⟩ and |1⟩. The 𝑅𝑌 gate rotates the qubit state around the Y-axis. And the Hadamard gate brings a qubit into a state of superposition.

But if quantum operators transform the qubit state, how could one possibly describe the potential energies of a system?

Throughout the complete first volume, we were good with the abstract notion of the waveform and its normalization. Later, we got to know the polar form that derives from it. We were solely interested in the computational implications, not quite in the physical interpretation.

This will change now because we want to employ a physical property.

We repeatedly emphasized that particles behave like waves. The first thing to note is that we are not talking about any arbitrary wave but electromagnetic waves.