QTM102 · The Math You Need: Vectors, Matrices and Probability

Categories: Emerging Technology
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About Course

Learn exactly the math quantum computing uses, and no more: vectors, complex numbers, matrices and probability, practiced step by step in a free Python notebook.

Explore · 4 hours · 4 lessons, a lab, an assessed assignment and a portfolio piece

Who it is for

Learners who are comfortable with high-school algebra and want the mathematical tools to follow quantum circuits with confidence.

Prerequisites

QTM101 is recommended; high-school algebra is required.

What you will be able to do

  • Represent qubit states as vectors and compute their lengths and inner products
  • Perform basic complex-number arithmetic, including magnitude and conjugate
  • Multiply matrices and vectors by hand and in NumPy to apply simple gates
  • Compute measurement probabilities and expected results from state amplitudes

Lessons

  • Lesson 1 · Vectors and complex numbers
  • Lesson 2 · Matrices as operations
  • Lesson 3 · Probability and multiple qubits
  • Lesson 4 · Lab and assignment

Lab: Quantum math with NumPy

You build qubit states as NumPy arrays, check that they are normalized and apply gate matrices with matrix multiplication. You compute measurement probabilities and then simulate 1,000 measurements with random sampling to compare the counts with theory. You finish by building a two-qubit state with the Kronecker product.

Free tools: Google Colab (free) with Python and NumPy

Assessed assignment

Complete a problem set of ten exercises covering vectors, complex numbers, matrix-vector multiplication, normalization, probabilities and tensor products. Solve each exercise by hand first, showing your steps, and then verify it in your Colab notebook. For two of the exercises, simulate 1,000 measurements and compare the observed frequencies with the theoretical probabilities. Write a short paragraph explaining any difference you see.

Criterion Weight What excellent work looks like
Correct hand calculations 35% All ten exercises are solved correctly with clear, logical steps.
Notebook verification 25% Notebook reproduces every answer, with readable code and comments.
Simulation and interpretation 25% Simulated frequencies are compared with theory and differences are explained using sampling variation.
Presentation 15% Work is organized, labeled and uses consistent notation.

Portfolio piece

A commented Colab notebook that implements qubit states, gate matrices, probabilities and tensor products from scratch.

Self-paced, 12-month access. Questions are answered in writing through the student panel. A completion record is issued when you finish the course.

Next step

Continue with QTM103 · Qubits, Superposition and Entanglement · 6 hours · $42.00

Continue to the next course

Prefer the whole program? Program in Quantum Computing Foundations · $277.00 (10% less than buying the courses separately)

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What Will You Learn?

  • Represent qubit states as vectors and compute their lengths and inner products
  • Perform basic complex-number arithmetic, including magnitude and conjugate
  • Multiply matrices and vectors by hand and in NumPy to apply simple gates
  • Compute measurement probabilities and expected results from state amplitudes

Course Content

QTM102 · The Math You Need: Vectors, Matrices and Probability (4 h)
Learn exactly the math quantum computing uses, and no more: vectors, complex numbers, matrices and probability, practiced step by step in a free Python notebook.

  • Lesson 1 · Vectors and complex numbers
  • Lesson 2 · Matrices as operations
  • Lesson 3 · Probability and multiple qubits
  • Lesson 4 · Lab and assignment
  • QTM102 Assessment · The Math You Need: Vectors, Matrices and Probability
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