# Boltzmann Law: Physics to Computing (edX)

##### Start Date
Mar 27th 2023
Course Auditing
Categories
Effort
Certification
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This course is designed for students who have an undergraduate degree in engineering or the physical sciences, specifically differential equations, and linear algebra.
Misc

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

What you'll learn

- Boltzmann Law

- Boltzmann Machines

- Transition Matrix

- Quantum Boltzmann Law

- Quantum Gates

### Syllabus

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

5.3. Grover Search

5.4. Shor's Algorithm

5.5. Feynman Paths

5.6 Summary for Exam 3

Epilogue

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