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Solving the Hard Problems in AI & Artificial Intelligence

Learn about Solving the Hard Problems in this comprehensive AI & Artificial Intelligence tutorial. Optimization in the quantum age.

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1From Physics to Logic

QAOA uses the laws of physics to solve logical problems. By mapping a cost function to the energy of a quantum system, we can use the 'natural' tendency of the system to find the lowest energy state.

2The p-level Advantage

As we increase the number of layers in QAOA, the algorithm theoretically converges to the exact solution. However, deeper circuits are more susceptible to noise on current hardware.

3Step-by-Step Breakdown

Combinatorial Opt. Finding the best solution from a finite set of possibilities.

Cost Hamiltonian. We encode the problem we want to solve into a Hamiltonian matrix.

Mixer Hamiltonian. The mixer allows the system to explore different states.

QAOA Circuit. Applying cost and mixer layers alternately.

Repetitions. The depth 'p' determines the quality of the approximation.

Optimization. Training beta and gamma parameters to find the minimum energy.

Check. What happens as the depth 'p' of QAOA increases?

  • Result gets worse
  • Result approaches optimum

Max-Cut Problem. Partitioning nodes of a graph to maximize the number of edges between them.

Adiabatic Link. QAOA is a trotterized version of adiabatic quantum computing.

End. QAOA mastered.

Compute a Real MaxCut Cost. Finish counting how many graph edges get cut by a given partition — the objective QAOA optimizes.

Pascual Vila

Pascual Vila

Frontend Instructor // Code Syllabus

Common Pitfalls & Errors

The Error //

Data Leakage

# Wrong scaler.fit(X) X_train = scaler.transform(X_train) X_test = scaler.transform(X_test) # Correct scaler.fit(X_train) X_train = scaler.transform(X_train) X_test = scaler.transform(X_test)

The Solution //

Never use data from the validation or test sets to train your model. This includes fitting scalers or imputers on the entire dataset before splitting.

The Error //

Overfitting on small datasets

// Solution: Use techniques like Dropout, L2 Regularization, or Early Stopping to prevent the model from overfitting the training data.

The Solution //

Training a complex model (like a deep neural network) on a very small dataset usually leads to memorization instead of generalization. Use simpler models or apply strong regularization.

Lesson Glossary

[01]Hamiltonian

An operator representing total energy.

Code Preview
// Hamiltonian context

[02]Max-Cut

A graph optimization problem.

Code Preview
// Max-Cut context

[03]Adiabatic

A slow process that stays in the ground state.

Code Preview
// Adiabatic context

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