I'm a **quantum machine learning (QML)** researcher in Maria Schuld's
group at Xanadu. I'm interested in quantum algorithms, statistical
learning theory, and symmetry.
QML is a research area that explores the
interplay of ideas from quantum computing and machine learning.
This goes in both directions.
We can ask if the unique abilities of quantum computers can help us
train machine learning models faster, or on quantum data where they
are a better fit than classical models.
On the other hand, classical machine learning can give us insights
into quantum algorithms and the capabilities of quantum computers for
generalization.

This page give an informal overview of QML. For a more detailed introduction to quantum computing, see this page. Once you've read that, you may want to check out the companion tutorial on QML.

*Image/style credits to Tarik Elkhateeb and the PennyLane.ai What is QML? page.*

## The two-way street

The success story of modern deep learning is also the story of
hardware it runs on: the parallel GPUs and architectural innovations
which allow an LLM, for instance, to learn on an internet-sized dataset.
In QML, it is natural to start with the hardware at our
disposal, namely *noisy quantum circuits*, and ask if the associated
architecture is superior for certain tasks. This leads to a class of
algorithms called **variational quantum circuits (VQC)**.

On the other hand, we can use classical tools such as
**Fourier series** and **kernel learning** to characterize quantum
models. This provides important insights into their expressivity,
generalization and training mechanics. This
shows that QML really is a two-way street!

## Performance from NISQ to ISQ

One advantage of vartional circuits is that they run on the devices we have now, and can be easily simulated. Because these devices and simulations are small, we cannot rely on theoretical arguments which only hold for very large quantum computers. Instead, we need to use benchmarks—performance on real datasets—to see how they stack up, as is standard practice in classical ML.

The quantum devices you can find in the lab right now are error-prone
and modest in size. They
can implement small VQCs and prove quantum advantage for
other tasks, but we don't expect them to provide useful applications
just yet.
In the not-too-distant future, we hope these **Noisy Intermediate-Scale
Quantum (NISQ)** computers will be replaced by **Intermediate-Scale
Quantum (ISQ)** ones, which are small but fault-tolerant.
Finding useful QML algorithms for these devices is an open problem.

## Symmetry and inductive bias

If we defeat these constraints (on size and noise), we will be rewarded with the "holy
grail": a **Fault-Tolerant Quantum Computer (FTQC)**, where we can run
large-scale quantum computations with negligible error. But even if we had such a device,
what would we do with it? Variational circuits come from asking: what
can we do with this hardware? The question now is: what do quantum
computers do best? This is a very different beast.

Quantum complexity theory suggests that quantum computers
are best at discovering **hidden symmetries**. The quantum computer
queries multiple items, attaches a phase to each, and interferes these
phases cleverly to extract the result. Shor's algorithm for breaking
RSA is a famous example.

It turns out that quantum computers can use similar techniques to
*learn hidden symmetries from data*. Many real-world problems display
approximate symmetry, so we expect this not only to be fast, but
useful! Turning things around, what does this teach us about quantum
computing? Using tools from ML, it tells us they have an **inductive
bias**, certain guesses they like to make more than
others. Characterizing these biases will tell us what other problems
quantum computers might be good at learning, and forms an exciting
area for future research.

โQC for dummies ยท โQML for dummies ยท ๐ฅ๐ข๐ญ๐ฑ๐๐ฏ๐ ๐ฅ