Lecture 5.1 - Building a Quantum Classifier

Last updated Jun 24, 2022

• Type note
• Status good
• On quantum computing machine learning
• By qiskit

• URL:: https://learn.qiskit.org/summer-school/2021/lec5-1-building-quantum-classifier
• Links:: 2021 Qiskit Global Summer School
• Instructor:: Amira Abbas

• 🕒 00:58 Hilbert Space is a big space!
  • Quantum Computing gives us excess to exponential state space where we can apply computations.
  • With just $275$ qubits, we can represent more states than the number of atoms in the observable universe.
• 🕒 01:55 Interference is more important/interesting as compared to exponential state space.
• 🕒 03:07 Quantum Machine Learning paradigms
  
• 🕒 05:15 How quantum computers can fit into the framework of classical machine learning?
  
• 🕒 06:35 Near-term vs fault-tolerant
  • Near-term devices are those noisy devices that are available today.
  • Fault-tolerant are those that will be error-free in the future, hopefully.
• 🕒 07:33 What can we do now with NISQ devices?

🕒 07:58 Variational models

• A quantum circuit that contains some parameters in it that we can train/optimize.
• 🕒 09:33 Names of Variational models

🕒 10:27 A first attempt at QML

• We can use a variational circuit as a classifier.
• 🕒 12:09 Task: Train a quantum circuit on labelled samples in order to predict labels for new data
• Steps
• 🕒 12:46 Step 1: Encode the classical data into a quantum state
• 🕒 13:09 Step 2: Apply a parameterized model
• 🕒 13:26 Step 3: Measure the circuit to extract labels
• 🕒 13:42 Step 4: Use optimization techniques (like gradient descent) to update model parameters

🕒 14:13 Data encoding

• How to encode classical data into a quantum system?
• This is still an open question/problem.
• It depends on the problem.
• 🕒 15:18 Basis encoding
  • Encode classical data into computational basis states.
• 🕒 17:15 Amplitude encoding
  • Encode classical data into amplitude vectors.
  • Use a parameterized gate such that the resulting state encodes feature into its amplitudes.
• 🕒 20:05 Angle encoding
  • Encode classical data into angles with which we rotate qubits.
• 🕒 22:53 Higher order encoding
  • Here, we are encoding higher-orders of our data, by encoding products of features as angles.

🕒 25:34 Applying a variational model

• 
• How to design circuits? This is an open question/problem.
• 🕒 29:34 High-expressive variational circuit is not always advantageous.
• 🕒 30:18 Example of a typical variational model
  • 
• 🕒 33:32 How to extract labels from the model?
  • This is also an open question.
  • 🕒 34:20 Parity post-processing
    • This is for binary classification.
    • 
  • 🕒 39:42 Measuring the first qubit
    • We can only measure the first qubit to interpret the probability of our label.
    • 

🕒 43:58 Optimization

• 
• How to compute the gradient of a quantum circuit?
  • 
  • This is called the parameter shift rule.
• 🕒 47:29 Is this advantageous?
  • 🕒 48:40 Data encoding
    • We map our original data into a higher-dimensional space.
    • So we can think of this as a feature map, transforming our data from one space to another higher-dimensional space.
  • 🕒 51:05 We can think of quantum classifiers as linear classifiers in a feature space (recall support vector machines and their linear decision function)
    • At the moment, this doesn’t provide any known advantage.
• 🕒 52:13 Recap
• 🕒 53:32 What’s next?