Quantum meets AI

This course is about two fast-moving fields — quantum computing and artificial intelligence — and the places where they meet. The meeting goes in both directions, and it pays to keep them separate.

Direction 1: quantum for AI

Quantum machine learning (QML) asks whether quantum computers can learn from data better — faster, with fewer examples, or with more expressive models — than classical machine learning.

A helpful classification looks at two questions: is the data classical or quantum? and is the processing classical or quantum?

The bottom-right cell — learning directly from quantum data — is where the strongest evidence for advantage exists so far. Huang and colleagues (2022) showed, both in theory and in an experiment on a Google processor, that a learner with quantum memory could learn certain properties of physical systems from exponentially fewer experiments than any learner that must measure each experiment separately.

For classical data the picture is much less clear, for reasons we will study below.

What a quantum model looks like

The most common QML model today is the variational (or parameterised) quantum circuit:

1. Encode an input $x$ into a quantum state using gates whose angles depend on $x$.
2. Process it with gates whose angles are trainable parameters $\theta$.
3. Measure to obtain an output, such as the expected value of some observable, $f_\theta(x)$.
4. A classical optimiser adjusts $\theta$ to reduce a loss function — exactly as in training a neural network.

This hybrid quantum–classical loop is sometimes called a quantum neural network. You will build one in Module 11 of this course and study it in depth in the Advanced course.

The open challenges

Three results shape how researchers think about QML with classical data:

• Trainability. McClean et al. (2018) showed that for broad classes of randomly initialised circuits, gradients shrink exponentially with the number of qubits — a barren plateau — making training effectively impossible at scale. Designing circuits that avoid this is an active research area.
• Dequantisation. In 2018 Ewin Tang found a classical algorithm for recommendation systems that matched the performance of a celebrated quantum algorithm up to polynomial factors, removing its claimed exponential advantage. Several other QML speed-ups have since been "dequantised" in the same way.
• Data loading. As you saw in the previous lesson, encoding large classical datasets into quantum states can erase theoretical speed-ups.

Direction 2: AI for quantum

The other direction is already delivering results. Building and running a quantum computer involves hard problems that machine learning is good at:

• Decoding errors. Quantum error correction requires a classical decoder that infers which errors happened from indirect measurements, fast and accurately. In 2024, Google DeepMind's AlphaQubit — a transformer-based neural network — decoded surface-code data from Google's Sycamore processor more accurately than the leading conventional decoders.
• Calibration and control. Machine learning helps tune the thousands of control parameters of a quantum processor and design pulses that implement gates with lower error.
• Compilation. Learned methods help optimise and simplify circuits for specific hardware.

How this course is organised

To reason clearly about all of this you need solid foundations in both fields. The Foundation course builds them in order:

1. Mathematics you need — complex numbers, vectors, matrices, Dirac notation (Module 2).
2. Qubits, gates and circuits — including entanglement (Modules 3–6).
3. Algorithms where quantum computers provably help — Deutsch–Jozsa, Bernstein–Vazirani, Grover, the QFT (Modules 7–9).
4. Machine-learning essentials — for learners without an ML background (Module 10).
5. Your first QML model, trained and evaluated honestly against a classical baseline (Module 11).
6. Noise and today's hardware (Module 12).

The Advanced course then takes each of these threads to research depth.

Summary

• "Quantum for AI" (QML) uses quantum computers to learn; "AI for quantum" uses ML to build and run quantum computers.
• The strongest evidence for quantum learning advantage today involves quantum data; for classical data, advantage remains unproven.
• Variational circuits are trained like neural networks but face barren plateaus, dequantisation and data-loading challenges.
• AI for quantum — decoders, calibration, compilation — is already producing state-of-the-art results.