Introduction to Quantum Computing

Master the fundamentals of quantum computing with our undergraduate-level course.

Detailed standards coverage

The course sequence is organized around the standards, course frameworks, and topic progressions students are expected to master.

What this course covers

An introductory quantum computing path that builds the needed linear algebra while teaching quantum states, gates, measurement, and algorithms.

Best for learners who want the math and conceptual tools behind quantum computation without requiring a prior quantum mechanics course.

Built from a 53-topic current sequence spanning complex numbers, vectors, matrices, and quantum computing.

Course map: PhysicsGraph sequence, topic granularity, and prerequisite structure.

Your Learning Outcomes

From high school math (algebra and trigonometry) to quantum algorithms in a structured, mastery-based progression. No calculus required!

Complex Numbers

• Master complex number arithmetic in both rectangular and polar forms.

• Visualize complex numbers on the complex plane and understand their visual properties, including how polar form corresponds to rotations on the unit circle.

• Apply Euler's formula to convert between rectangular and polar representations.

• Calculate complex conjugates, modulus, and arguments.

Linear Algebra

• Execute vector operations and calculate dot products in real and complex vector spaces.

• Apply basic matrix operations including addition, subtraction, scalar multiplication, and multiplication.

• Construct linear combinations of vectors and apply basis concepts.

• Work with complex Hilbert spaces and calculate projections.

Quantum Postulates & Foundations

• Apply the four fundamental postulates of quantum mechanics to quantum systems.

• Construct and normalize quantum state vectors in a Hilbert space.

• Execute quantum measurements and predict measurement outcome probabilities.

• Analyze quantum state evolution using unitary operators.

• Understand the Many Worlds explanation through Mach-Zehnder experiments.

Quantum Bits & Circuits

• Master single-qubit quantum gates including Pauli matrices (X, Y, Z) and the Hadamard gate.

• Construct and analyze both classical and quantum circuits using the circuit model of computation.

• Trace quantum state evolution through matrix multiplication.

• Execute multi-qubit operations using tensor products.

Quantum Protocols & Algorithms

• Study fundamental quantum protocols including quantum teleportation and superdense coding.

• Apply Deutsch's algorithm to distinguish constant from balanced functions.

• Analyze multi-qubit quantum systems and entangled states.

• Compare computational advantages of quantum algorithms over classical approaches.

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