QKarma
← All coursesAdvanced · ~60 hours

Quantum Computing + AI: Advanced

Variational algorithms, QML, noise and error correction on real hardware

For learners who have completed the Foundation course (or pass the placement test) and want working depth in quantum algorithms, quantum machine learning and the realities of running them on noisy hardware.

What you'll be able to do

  • ✓Describe mixed states and noise with density matrices and quantum channels
  • ✓Explain Shor's algorithm end to end, including the classical post-processing
  • ✓Implement VQE and QAOA and diagnose optimisation problems such as barren plateaus
  • ✓Build and evaluate quantum kernel methods and quantum neural networks against classical baselines
  • ✓Apply error-mitigation techniques and explain the principles of quantum error correction
  • ✓Critically evaluate published quantum-advantage and QML claims

Syllabus

Module 1

Density Matrices and Quantum Channels

Mixed states, partial trace, fidelity and the maths of noise.

⌄

You will learn to

  • Represent pure and mixed states with density matrices
  • Compute reduced states with the partial trace
  • Describe noise as quantum channels using Kraus operators
  • Compute fidelity and trace distance between states
  1. ·Pure and mixed statesComing soon40 min
  2. ·The partial traceComing soon40 min
  3. ·Quantum channelsComing soon45 min
  4. ·Fidelity and trace distanceComing soon35 min

Module 2

Shor's Algorithm

From factoring to period finding, with the full classical and quantum pipeline.

⌄

You will learn to

  • Reduce factoring to order finding
  • Build modular exponentiation and apply phase estimation to find the order
  • Recover the period with continued fractions
  • Estimate the resources needed to factor cryptographically relevant numbers
  1. ·From factoring to order findingComing soon40 min
  2. ·The order-finding circuitComing soon50 min
  3. ·Continued fractions and post-processingComing soon35 min
  4. ·Resource estimates and cryptographyComing soon30 min

Module 3

Variational Algorithms: VQE and QAOA

Hybrid optimisation for chemistry and combinatorial problems.

⌄

You will learn to

  • State the variational principle and build a VQE loop
  • Map a molecular Hamiltonian (H₂) to qubits and estimate its ground-state energy
  • Encode Max-Cut as a cost Hamiltonian and implement QAOA
  • Choose ansätze and classical optimisers sensibly
  1. ·The variational principleComing soon35 min
  2. ·VQE for the hydrogen moleculeComing soon55 min
  3. ·QAOA for Max-CutComing soon50 min
  4. ·Ansätze and optimisersComing soon35 min

Module 4

Training Parameterised Circuits

Gradients on quantum hardware and the trainability problem.

⌄

You will learn to

  • Derive and apply the parameter-shift rule
  • Compare finite differences, parameter shift and SPSA
  • Explain barren plateaus and strategies to mitigate them
  1. ·The parameter-shift ruleComing soon40 min
  2. ·Comparing gradient methodsComing soon35 min
  3. ·Barren plateausComing soon40 min

Module 5

Quantum Kernel Methods

Feature maps, kernel estimation and quantum support vector machines.

⌄

You will learn to

  • Explain kernels and feature maps from classical ML
  • Estimate a quantum kernel with a fidelity circuit
  • Train and evaluate a QSVM, including kernel concentration effects
  1. ·Kernels and feature mapsComing soon35 min
  2. ·Quantum feature mapsComing soon40 min
  3. ·Quantum support vector machinesComing soon45 min

Module 6

Quantum Neural Networks and Hybrid Models

QNNs with Qiskit Machine Learning and PyTorch.

⌄

You will learn to

  • Build estimator- and sampler-based QNNs
  • Integrate a QNN as a PyTorch layer and train end to end
  • Compare expressivity and trainability with classical networks
  1. ·QNN architecturesComing soon40 min
  2. ·Hybrid models with PyTorchComing soon50 min
  3. ·Expressivity and trainabilityComing soon35 min

Module 7

Noise Models and Error Mitigation

Getting better answers from noisy hardware without full error correction.

⌄

You will learn to

  • Build noise models from device calibration data
  • Apply readout-error mitigation
  • Apply zero-noise extrapolation and dynamical decoupling
  • Quantify the sampling overhead of mitigation
  1. ·Building noise modelsComing soon40 min
  2. ·Readout-error mitigationComing soon35 min
  3. ·Zero-noise extrapolationComing soon40 min
  4. ·Dynamical decoupling and twirlingComing soon35 min

Module 8

Quantum Error Correction

From the repetition code to stabilisers and the surface code.

⌄

You will learn to

  • Protect against bit-flip and phase-flip errors with repetition codes
  • Describe codes with the stabiliser formalism
  • Explain the surface code, syndromes, decoding and thresholds
  1. ·Repetition codesComing soon40 min
  2. ·The Shor and Steane codesComing soon40 min
  3. ·The stabiliser formalismComing soon45 min
  4. ·The surface code and thresholdsComing soon45 min

Module 9

Running on Hardware in Practice

Transpilation, topology and IBM runtime primitives at depth.

⌄

You will learn to

  • Control transpiler optimisation levels, layouts and routing
  • Choose qubits using calibration data
  • Use Sampler and Estimator primitives with sessions and batches
  1. ·The transpiler in depthComing soon45 min
  2. ·Choosing qubits from calibration dataComing soon35 min
  3. ·Runtime primitivesComing soon40 min

Module 10

AI for Quantum

Machine learning applied to building and operating quantum computers.

⌄

You will learn to

  • Describe neural-network decoders for error correction
  • Explain ML-assisted calibration and control
  • Survey learned approaches to circuit optimisation and compilation
  1. ·Neural decodersComing soon40 min
  2. ·ML for calibration and controlComing soon35 min
  3. ·Learned circuit optimisationComing soon35 min

Module 11

Critical Reading of Quantum Claims

How to evaluate advantage claims, benchmarks and QML papers.

⌄

You will learn to

  • Distinguish quantum supremacy, advantage and utility experiments
  • Identify weak baselines, dequantisation and data-loading caveats
  • Write a structured critique of a published result
  1. ·SupremacyComing soon40 min
  2. ·Dequantisation and classical baselinesComing soon40 min
  3. ·Reading a QML paper criticallyComing soon35 min

Capstone

An independent study — either a QML model or a VQE/QAOA experiment — run on real IBM hardware with error mitigation, benchmarked against a classical baseline, and written up as a short technical report graded against a published rubric.