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This is an important metric, because it takes some time for the quantum operations to propagate, and so the depth of a circuit gives you an idea of how long the <coherence time> a hardware needs to support a given circuit.

Bibliography:
* https://quantumcomputing.stackexchange.com/questions/14431/whats-meant-by-the-depth-of-a-quantum-circuit
* https://quantumcomputing.stackexchange.com/questions/5769/how-to-calculate-circuit-depth-properly

\Image[https://github.com/Qiskit/qiskit/blob/0.45.1/docs/source_images/depth.gif?raw=true]
{source=https://github.com/Qiskit/qiskit/blob/0.45.1/docs/source_images/depth.gif}


Depth of a quantum circuit