Data encoding

Basis, angle and amplitude encoding: how classical data enters a circuit and what each choice costs.

You will learn to

Encode a 4-dimensional vector three different ways.
Compare qubit count and circuit depth per encoding.
Explain why encoding dominates many QML costs.

Encoding	Qubits for N features	Depth	Note
Basis	N (bits)	1	x = 0101 → \|0101⟩; only for binary data
Angle	N	1	feature xᵢ → ry(xᵢ) on qubit i; simple and hardware-friendly
Amplitude	log₂ N	O(N)	x becomes the statevector itself; exponentially compact, exponentially deep to prepare

Try it

Angle-encode (0.3, 1.2, 2.0, 0.7)

Four features, four qubits, one layer. The Bloch view shows each qubit tilted by its feature. Add a second layer of CNOTs and RYs to see how a feature map creates correlations the model can use.

OPENQASM 3.0;
include "stdgates.inc";
qubit[4] q;
ry(0.3) q[0];
ry(1.2) q[1];
ry(2.0) q[2];
ry(0.7) q[3];

Open in the IDE Open in the Playground

Quiz 1 · 10 XP

Amplitude encoding of 1024 features needs how many qubits?

Quiz 2 · 10 XP

Which statement about QML speed-ups is honest?

Key takeaway

Angle encoding is cheap and shallow, amplitude encoding is compact but deep. Always count the cost of getting data in before believing a speed-up.

Docs: encodings and feature maps

Up next: QAOA on a small graph

Encoding

Qubits for N features

Depth

Note

Basis

N (bits)

x = 0101 → |0101⟩; only for binary data

Angle

feature xᵢ → ry(xᵢ) on qubit i; simple and hardware-friendly

Amplitude

log₂ N

O(N)

x becomes the statevector itself; exponentially compact, exponentially deep to prepare