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PurdueX: Boltzmann Law: Physics to Computing

Provides a unified perspective connecting equilibrium statistical mechanics with stochastic neural networks and quantum computing.

5 weeks
5–6 hours per week
Instructor-paced
Instructor-led on a course schedule
Free
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Started Oct 30
Ends Dec 6
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Boltzmann Law: Physics to Computing

About this course

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A unique course that connects three diverse fields using the unifying concept of a state-space with 2^N dimensions defined by N binary bits. We start from the seminal concepts of statistical mechanics like entropy, free energy and the law of equilibrium that have been developed with the purpose of describing interacting systems occurring in nature. We then move to the concept of Boltzmann machines (BM) which are interacting systems cleverly engineered to solve important problems in machine learning. Finally, we move to engineered quantum systems stressing the phenomenon of quantum interference which can lead to awesome computing power.

At a glance

  • Institution: PurdueX
  • Subject: Engineering
  • Level: Advanced
  • Prerequisites:

    This course is designed for students in engineering or the physical sciences and have knowledge of differential equations and linear algebra.

  • Language: English
  • Video Transcript: English
  • Associated skills:State Space, Physics, Mechanics, Artificial Neural Networks, Machine Learning

What you'll learn

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  • Boltzmann Law
  • Boltzmann Machines
  • Transition Matrix
  • Quantum Boltzmann Law
  • Quantum Gates

Syllabus

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Week 1: Boltzmann Law

1.1 State Space

1.2 Boltzmann Law

1.3 Shannon Entropy

1.4 Free Energy

1.5 Self-consistent Field

1.6 Summary for Exam 1

Week 2: Boltzmann Machines

2.1. Sampling

2.2. Orchestrating Interactions

2.3. Optimization

2.4. Inference

2.5. Learning

Week 3: Transition Matrix

3.1. Markov Chain Monte Carlo

3.2. Gibbs Sampling

3.3. Sequential versus Simultaneous

3.4. Bayesian Networks

3.5. Feynman Paths

3.6 Summary for Exam 2

Week 4: Quantum Boltzmann Law

4.1. Quantum Spins

4.2. One q-bit Systems

4.3. Spin-spin Interactions

4.4. Two q-bit Systems

4.5. Quantum Annealing

Week 5: Quantum Transition Matrix

5.1. Adiabatic to Gated Computing

5.2. Hadamard Gates

5.3. Grover Search

5.4. Shor's Algorithm

5.5. Feynman Paths

5.6 Summary for Exam 3

Epilogue

Learner testimonials

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"The way that this professor explains the material very well. All of this was very new to me but he explained it in a way that made the course interesting and engaging. I also enjoy the quizzes after every lecture video. It’s very helpful in ensuring that I learn the material properly. " - Student, Fall 2020 semester

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