QKarma
← All coursesFoundation · ~40 hours

Quantum Computing + AI: Foundation

From qubits to your first hybrid quantum classifier

For developers, students and data/ML practitioners who want a rigorous but approachable start in quantum computing and quantum machine learning. No physics background is needed — every piece of mathematics is introduced before it is used.

What you'll be able to do

  • ✓Describe qubit states with Dirac notation, vectors and the Bloch sphere, and predict measurement probabilities with the Born rule
  • ✓Build and reason about circuits using single-qubit gates, CNOT and entanglement
  • ✓Explain why Deutsch–Jozsa, Bernstein–Vazirani and Grover's algorithm outperform their classical counterparts, and where the speed-up comes from
  • ✓Write, simulate and run circuits with Qiskit — including on real IBM quantum hardware
  • ✓Explain the core ideas of supervised machine learning and train a small hybrid quantum-classical classifier
  • ✓Evaluate claims about quantum advantage critically, with an accurate picture of today's noisy hardware

Syllabus

Module 1

Why Quantum + AI?

What quantum computers are, what they are not, and where they might matter for AI.

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You will learn to

  • Distinguish classical bits from qubits at an intuitive level
  • Name the problem classes where quantum speed-ups are proven, expected, or unlikely
  • Separate evidence-based claims about quantum computing from hype
  1. ·What is a quantum computer?Free preview20 min
  2. ·Where quantum helps — and where it doesn'tFree preview25 min
  3. ·Quantum meets AIFree preview20 min

Module 2

The Mathematical Toolkit

Complex numbers, vectors, matrices and probability — exactly the maths quantum computing needs, and no more.

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You will learn to

  • Add, multiply and find the magnitude of complex numbers, including in polar form
  • Compute inner products, norms and matrix-vector products for small vectors and matrices
  • Recognise unitary matrices and explain why they preserve length
  • Read and write states in Dirac (bra-ket) notation
  1. ·Complex numbers35 min
  2. ·Vectors and inner products35 min
  3. ·Matrices as transformations40 min
  4. ·Dirac notation30 min

Module 3

Qubits, Superposition and Measurement

The state of a single qubit, the Born rule, and the Bloch sphere.

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You will learn to

  • Write a general single-qubit state and state the normalisation condition
  • Compute measurement probabilities with the Born rule, in the computational and other bases
  • Explain the difference between global and relative phase
  • Map any pure single-qubit state to a point on the Bloch sphere
  1. ·The qubit30 min
  2. ·Measurement and the Born rule35 min
  3. ·Global and relative phase30 min
  4. ·The Bloch sphere35 min

Module 4

Single-Qubit Gates

Pauli, Hadamard, phase and rotation gates as unitary matrices and as rotations of the Bloch sphere.

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You will learn to

  • Apply X, Y, Z, H, S and T gates to states by matrix multiplication
  • Interpret each gate as a rotation of the Bloch sphere
  • Use RX, RY, RZ rotations and the general U gate
  • Compose gates and verify circuit identities such as HZH = X
  1. ·The Pauli gatesComing soon30 min
  2. ·The Hadamard gateComing soon30 min
  3. ·Phase gates S and TComing soon25 min
  4. ·Rotation gates and the U gateComing soon35 min
  5. ·Circuit identitiesComing soon30 min

Module 5

Multiple Qubits and Entanglement

Tensor products, CNOT, Bell states, no-cloning and teleportation.

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You will learn to

  • Build multi-qubit states with the tensor product and read little-endian qubit ordering
  • Apply CNOT, CZ and SWAP and construct the four Bell states
  • Test whether a two-qubit pure state is entangled
  • Prove the no-cloning theorem and walk through quantum teleportation
  1. ·Tensor productsComing soon35 min
  2. ·Two-qubit gatesComing soon35 min
  3. ·Entanglement and Bell statesComing soon40 min
  4. ·The no-cloning theoremComing soon25 min
  5. ·Quantum teleportationComing soon40 min

Module 6

Circuits in Qiskit and Real Hardware

Writing circuits in Qiskit, simulating them, and running them on IBM quantum computers.

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You will learn to

  • Build, draw and simulate circuits with Qiskit
  • Explain shots, counts and sampling error
  • Transpile a circuit for a real device and interpret its coupling map
  • Submit a job to IBM Quantum hardware and compare with simulation
  1. ·Your first Qiskit circuitComing soon35 min
  2. ·ShotsComing soon30 min
  3. ·Transpilation basicsComing soon30 min
  4. ·Running on IBM quantum hardwareComing soon40 min

Module 7

Oracle Algorithms

Phase kickback, Deutsch–Jozsa and Bernstein–Vazirani — the first provable quantum advantages.

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You will learn to

  • Explain the oracle (query) model and phase kickback
  • Trace Deutsch's and the Deutsch–Jozsa algorithm step by step
  • Implement Bernstein–Vazirani and compare query complexity with classical approaches
  1. ·Oracles and phase kickbackComing soon35 min
  2. ·The Deutsch–Jozsa algorithmComing soon40 min
  3. ·The Bernstein–Vazirani algorithmComing soon35 min

Module 8

Grover's Search

Amplitude amplification, its geometry, and its quadratic speed-up.

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You will learn to

  • Build Grover's oracle and diffusion operator
  • Explain amplitude amplification geometrically as a rotation
  • Compute the optimal number of iterations and explain why over-rotating hurts
  • State why Grover's speed-up is quadratic, not exponential
  1. ·The unstructured search problemComing soon25 min
  2. ·The Grover operatorComing soon40 min
  3. ·The geometry of amplitude amplificationComing soon35 min
  4. ·Grover in practiceComing soon35 min

Module 9

The Quantum Fourier Transform and Phase Estimation

The QFT as a circuit and its central role in phase estimation.

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You will learn to

  • Describe the QFT and build its circuit for small n
  • Explain quantum phase estimation and its precision/qubit trade-off
  • Connect phase estimation to Shor's algorithm (developed in the Advanced course)
  1. ·Fourier intuitionComing soon30 min
  2. ·The QFT circuitComing soon40 min
  3. ·Quantum phase estimationComing soon40 min

Module 10

Machine Learning Essentials

Supervised learning, loss functions, gradient descent and neural networks — the AI half of the course.

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You will learn to

  • Frame a supervised learning problem with features, labels and a loss
  • Derive and run gradient descent on a simple model
  • Explain overfitting, train/test splits and regularisation
  • Describe how a small neural network computes and learns
  1. ·Supervised learningComing soon30 min
  2. ·Loss functions and gradient descentComing soon40 min
  3. ·Generalisation and overfittingComing soon30 min
  4. ·Neural networksComing soon40 min

Module 11

First Steps in Quantum Machine Learning

Encoding data into qubits, parameterised circuits, and a hybrid classifier.

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You will learn to

  • Compare basis, angle and amplitude encoding and their costs
  • Build a parameterised (variational) circuit and compute an expectation value
  • Train a hybrid quantum-classical classifier on a small dataset
  • Assess the result honestly against a classical baseline
  1. ·Encoding classical dataComing soon35 min
  2. ·Variational circuitsComing soon35 min
  3. ·A hybrid quantum-classical classifierComing soon45 min
  4. ·Baselines and honest evaluationComing soon25 min

Module 12

Noise and the NISQ Era

Why real qubits are imperfect, how that shows up in results, and what it means for applications today.

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You will learn to

  • Name the main error sources — decoherence (T1/T2), gate errors, readout errors
  • Recognise noise signatures in hardware results
  • Explain what "NISQ" means and why error correction is the long-term path
  1. ·Sources of noiseComing soon30 min
  2. ·Seeing noise in resultsComing soon30 min
  3. ·NISQ and the road to fault toleranceComing soon25 min

Capstone

Design a Bell-state and a 2-qubit Grover experiment, run both on a simulator and on a real IBM quantum device, and write a short report that compares the ideal, simulated and hardware results and explains the differences in terms of noise.