*by Amara Graps*

If you’ve entered the quantum computing field via hybrid quantum-classical computing, then you’ve been introduced to Quantum Machine Learning (QML), whether you knew it or not.

AI / QML is inside of quantum technology applications from top to bottom. It is inside most hybrid quantum-classical Use Cases. It’s so pervasive in Quantum Technology, that you may have difficulty understanding where AI ends and quantum begins, or where quantum ends, and AI begins. Indeed, in the new European Commission Report: (Dis)Entangling the Future, which recommends topics for EIC’s Quantum Technologies portfolio, their conclusions state:

A topic that also stood out was the interrelation between AI and Quantum. That is, how the field of AI can help the field of quantum and also, how quantum can serve the field of AI.

So, I thought I’d begin with a QML conceptual foundation that provided clarity for me.

**Chart-of-Clarity: -Which- QML?**

First, the data definitions.

Classical data is any represented by 0/1 bits. Therefore, images, text, graphs, images from biological studies, medical data, stock values, attributes of molecules, and collision traces from high energy physics experiments are examples of classical data.

Quantum data is -any- that is encoded in qubits, or higher dimensional analogs. The states |0>, |1>, or any normalized complex linear superposition of these two, can be used to represent a qubit. Quantum sensing, quantum metrology, quantum networks, quantum control, or even quantum analog-digital transduction, are examples of physical processes, from which the states in this case have information. Additionally, quantum data can be used to solve quantum computer problems, for example, preparing the ground states of different Hamiltonians.

Depending on whether one believes that the data was created by a classical or quantum system, as well as whether the computer processing the data is a classical or quantum system, there are four ways to combine machine learning and quantum computing.

**Classical-Classical**: The data in the scenario Classical-Classical is handled conventionally. This is a classic machine learning strategy; in this instance, it relates to machine learning with methods taken from quantum information research. For example, neural network training has made use of tensor networks, which are quantum-inspired. These are classical methods that can analyze classical data, which are built to address quantum many-body phenomena.

**Classical-Quantum:** In the scenario Classical-Quantum, traditional datasets are examined using quantum computing. Images and text observations from classical computers are sent into a quantum device for analysis. The community has provided numerous solutions for the construction of quantum algorithms for use in data mining, which is the main goal of this methodology. They could be completely original works motivated by the properties of quantum computing, or they could be modifications of conventional machine learning models to work with quantum algorithms. An example is handwritten digits, which can be mapped to quantum states for classification on a quantum computer.

**Quantum-Classical**: Quantum-Classical explores the potential applications of machine learning to quantum computing. For example, we can use machine learning to analyze the quantum measurement data, if we want to gain a comprehensive explanation of the condition of a computing device from a few measurements. Machine learning has uses in differentiating between manipulations performed by a quantum experiment and quantum states produced by a quantum source.

**Quantum-Quantum:** The Quantum-Quantum scenario looks at how a quantum device processes quantum data. For example, molecular ground state data can be classified directly on a quantum computer. The Quantum-Quantum scenario could be interpreted in two ways.

- A quantum experiment using a quantum system and the subsequent input of those experimental measurements into a different quantum computer yielding new information.
- A quantum computer simulates the behavior of the quantum system. Then it uses the state of the system as an input to a QML algorithm, which is run on the same quantum computer.

These scenarios tell you what to look for when you read a paper and wonder: where does that QML element fit in in the proposed solution? For investors, you will be technically better armed for your discussions. From the GQI perspective, QML appears inside of the Top Stack, the Hardware Stack, and the Mid Stack. It also has an important role in Quantum Simulators and in the User Community.

**Some QML Review Papers and another QML Book with a Course**

Who was the originator of the chart-of-clarity to sort out the quantum+AI interdependencies?

Several very good review papers pointed to the 2017, 1^{st} edition of Schuld and Petruccione’s text: Machine Learning with Quantum Computers, which is in its 2^{nd} edition now. The authors themselves point to a 2006 conference paper by Esma Aïmeur, Gilles Brassard & Sébastien Gambs : Machine Learning in a Quantum World

To help you build your QML expertise, I recommend these QML Reviews:

- Otterbach et al., 2017, Unsupervised Machine Learning on a Hybrid Quantum Computer
- Benedetti et al., 2019, Parameterized quantum circuits as machine learning models
- Cerezo et al., 2021, Challenges and Opportunities in Quantum Machine Learning
- Carleo et al., 2019, Machine learning and the physical sciences
- Meyer et al., 2024, A Survey on Quantum Reinforcement Learning

And a book, which comes with a course:

- Book: Hands-On Quantum Machine Learning With Python Volume 1: Get Started Dr. Frank Zickert (book at github) with a course

**Fast QML Progress**

These materials reflect how fast the field is progressing. Between 2017 and 2021, the text authors: Schuld and Petruccione, note the developments in their book’s 2021 preface:

Variational circuits, machine learning models derived from quantum circuits that depend on adaptable classical “control” parameters, have become a central focus of research. The training of such “quantum models” is facilitated by software libraries such as PennyLane, TensorFlow Quantum and Yao, which provide simulators and cloud access to quantum hardware. In other words, quantum machine learning is one of the first fields that is not only done on paper but also tested on real devices. Finally, a lot of progress has been made in our theoretical understanding of what happens when quantum computers learn from data […]

The authors are likely discussing amongst themselves the prospect of an updated edition of their textbook for today.

In the 2023+ hybrid quantum-classical research articles, you’ll likely read successes with quantum versions of machine learning algorithms exceeding the classical versions on small subsets of the datasets. For example: “*The VQC obtains a greater advantage over certain classical classifiers when implemented on a quantum computer with a smaller circuit depth*” Today’s results are limited by quantum RAM, which facilitates the mapping of classical input to a quantum computer.

Today’s results are in contrast to those in 2021, when you were likely to find conclusions similar to: *both the simulator and the real quantum computer have been unable to present results in less time than a classical computer.*

I will continue to use this Chart-of-Clarity to describe QML results. I hope it provides clarity for you too.

(*) This GQI Presentation summarizes the State of Play of Quantum Software, available in the Member’s area for GQI customers*. If you are interested, please don’t hesitate to contact **info@global-qi.com**.*

September 24, 2024