Tutorial
Machine Learning With Quantum Computers
Maria Schuld · Juan Carrasquilla
Moderator s: Aram Harrow · Asja Fischer
Quantum computing, a discipline that investigates how computing changes if we take into account quantum effects, has turned into an emerging technology that produced the first generation of hardware prototypes. In search of applications for these new devices, researchers turned to machine learning and found a wealth of exciting questions: Do machine learning algorithms gain a better computational complexity if we outsource parts of them to quantum computers? How does the problem of empirical risk minimisation change if our model class is made up of quantum algorithms? How does quantum hardware fit into AI pipelines? And, vice versa, can machine learning help us to study the behaviour of quantum systems?
In this tutorial we want to unpack these questions and sketch the landscape of preliminary answers found so far. For example, we will look at carefully constructed learning problems for which quantum computers have a provable complexity advantage, and motivate why it is so hard to make conclusive statements about more natural problem settings. We will explore how data can be represented as physical states of quantum systems, and how manipulating these systems leads to algorithms that are just kernel methods with a special kind of Hilbert space. We will see that quantum devices can be trained like neural networks, and that existing opensource software seamlessly integrates them into deep learning pipelines. Finally, we will understand how the deep connections between neural networks and quantum wave functions allow us to use machine learning techniques to understand quantum systems themselves.
The tutorial targets a broad audience, and no prior knowledge of physics is required.
Schedule
Mon 5:00 a.m.  5:05 a.m.

What to Expect
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intro
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We’ll give you an overview of what will be covered in this tutorial, what skills are helpful to follow, and what we’d like you to have learnt in the end. 
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Mon 5:05 a.m.  5:26 a.m.

Can Quantum Computers Help with Machine Learning?
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Talk
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SlidesLive Video This introduction wants to give you an intuition for the main challenge of quantum machine learning: to find out how machine learning could potentially be innovated by technology based on (ever so subtly) different physics principles, if we only have access to smallscale prototypes and mathematical theory. You’ll also learn about two important paradigms in quantum computing, the nearterm and faulttolerant approaches, and about some popular research areas within QML. 
Maria Schuld 🔗 
Mon 5:26 a.m.  5:40 a.m.

Q&A and SelfLearning
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Q&A
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We’ll send you out to gather as much information on QML as you can find in a few minutes. We’ll then discuss your first impressions, and try to clarify immediate questions. 
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Mon 5:40 a.m.  6:15 a.m.

Quantum Computers as Samplers from Special Distributions
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talk
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SlidesLive Video This section gives you a few insights into the mathematical apparatus of quantum computing. You will learn that quantum computers are samplers, and that we can describe expected outcomes of the samples using matrixvector multiplications, that can be interpreted as algorithms or “quantum circuits”. You will also hear a few fleeting comments on why quantum theory is different from classical probability theory. 
Maria Schuld 🔗 
Mon 6:15 a.m.  6:30 a.m.

Q&A + exercise
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Q&A
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Again we will answer questions that popped up, and give you an exercise that QML scientists were initially faced with: How would you use quantum computers for machine learning? You can get creative! 
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Mon 6:30 a.m.  6:50 a.m.

Using Quantum Computations as Machine Learning Models
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Talk
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SlidesLive Video A lot of QML research approaches the question you just tried to solve by interpreting quantum computations as machine learning models. Using the PennyLane software framework, we will show you practically how this can look like for generative and discriminative models. You’ll also see that we can compute gradients of our models, which means that they can be used as parts of deep learning pipelines. 
Maria Schuld 🔗 
Mon 6:50 a.m.  7:10 a.m.

Q&A
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Q&A
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We’ll answer your questions and let you play around with a notebook that deepens the code demonstration further. 
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Mon 7:10 a.m.  7:25 a.m.

Break
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Break
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Mon 7:25 a.m.  7:51 a.m.

What are Quantum Models?
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TAlk
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SlidesLive Video An important result in recent years was that some “quantum models” are just kernel methods: encoding the data into quantum states is a feature map, and the rest of a quantum algorithm defines a linear decision boundary. We discuss important consequences of this link and give you a glimpse of some “quantum kernels”. 
Maria Schuld 🔗 
Mon 7:51 a.m.  8:00 a.m.

Q&A
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Q&A
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What you have just learnt may have been a bit overwhelming, so here is some time to clarify the basics by answering your questions. 
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Mon 8:00 a.m.  8:43 a.m.

What ML Can Do For Quantum Manybody Physics
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Talk
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SlidesLive Video The last section is a little more “physics” themed, and shows how the connection between machine learning models and quantum states works the other way around: we can use neural networks as an ansatz to compress and learn our description of quantum systems. 
Juan Carrasquilla 🔗 
Mon 8:43 a.m.  8:55 a.m.

Q&A
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Q&A
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This is a final space for your questions. 
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Mon 8:55 a.m.  9:00 a.m.

Closing Remarks
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Talk
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SlidesLive Video We will give you pointers on how to start your quantum machine learning journey if you want to know more. 
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