toc.yaml

#  === Structure of the Qiskit Textbook ===
#
# This textbook is organised into 'courses', which are ordered lists of
# 'sections'. Sections are the smallest unit of content in this textbook,
# i.e. a single Jupyter notebook which is converted to a single web page.
#
# Below is a fake example of a simple course.
#
# - title: My course
#   url: /my-course   # pages in this course will have urls starting with
#                     # 'https://learn.qiskit.org/course/my-course'
#   sections:  # ordered list of notebooks
#     - title: My page  # Appears at top of page and in left sidebar
#       id: my-page     # Stem of the url for this page on the website,
#                       # i.e. this page will have url 'https://learn.qiskit.org/course/my-course/my-page'
#       uuid: a5a86ddc-b519-11ec-b909-0242ac120002  # Unique ID for
#                       # website software to identify pages if names change.
#                       # Generate new ids with https://www.uuidgenerator.net
#       url: /my-course/my-notebook  # Path to source notebook, relative to this file


- title: Basics of quantum information
  url: /basics
  sections:
    - title: Single systems
      id: single-systems
      uuid: dd5680be-7490-401e-9e68-c1ec7d0f5d61
      url: /basics/single-systems
    - title: Multiple systems
      id: multiple-systems
      uuid: 327b128f-4fec-410a-a3f9-079939002bf2
      url: basics/multiple-systems
    - title: Circuits, protocols, and games
      id: circuits-protocols-games
      uuid: 57d5452e-85cd-40f8-a290-11466213c1a6
      url: basics/circuits-and-protocols


- title: Prerequisites
  url: /ch-prerequisites
  sections:
    - title: Setting Up Your Environment
      id: environment-setup-guide-to-work-with-qiskit-textbook
      uuid: a5a86ddc-b519-11ec-b909-0242ac120002
      url: /ch-prerequisites/setting-the-environment
    - title: Python and Jupyter Notebooks
      id: introduction-to-python-and-jupyter-notebooks
      uuid: a9f5ea68-b519-11ec-b909-0242ac120002
      url: /ch-prerequisites/python-and-jupyter-notebooks


- title: Quantum States and Qubits
  url: /ch-states
  sections:
    - title: Introduction
      id: introduction
      uuid: afcc559e-b519-11ec-b909-0242ac120002
      url: /ch-states/introduction
    - title: The Atoms of Computation
      id: the-atoms-of-computation
      uuid: b31c20ee-b519-11ec-b909-0242ac120002
      url: /ch-states/atoms-computation
    - title: Representing Qubit States
      id: representing-qubit-states
      uuid: b81717ca-b519-11ec-b909-0242ac120002
      url: /ch-states/representing-qubit-states
    - title: Single Qubit Gates
      id: single-qubit-gates
      uuid: bd4334a4-b519-11ec-b909-0242ac120002
      url: /ch-states/single-qubit-gates
    - title: The Case for Quantum
      id: the-case-for-quantum-computers
      uuid: c0bbff62-b519-11ec-b909-0242ac120002
      url: /ch-states/case-for-quantum


- title: Multiple Qubits and Entanglement
  url: /ch-gates
  sections:
    - title: Introduction
      id: introduction
      uuid: c50f4c90-b519-11ec-b909-0242ac120002
      url: /ch-gates/introduction
    - title: Multiple Qubits and Entangled States
      id: multiple-qubits-and-entangled-states
      uuid: c7cfe502-b519-11ec-b909-0242ac120002
      url: /ch-gates/multiple-qubits-entangled-states
    - title: Phase Kickback
      id: phase-kickback
      uuid: cb7353ec-b519-11ec-b909-0242ac120002
      url: /algorithms/phase-kickback
    - title: More Circuit Identities
      id: basic-circuit-identities
      uuid: ce8ce75a-b519-11ec-b909-0242ac120002
      url: /ch-gates/more-circuit-identities
    - title: Proving Universality
      id: proving-universality
      uuid: d15d3548-b519-11ec-b909-0242ac120002
      url: /ch-gates/proving-universality
    - title: Classical Computation on a Quantum Computer
      id: classical-computation-on-a-quantum-computer
      uuid: d4f6e424-b519-11ec-b909-0242ac120002
      url: /ch-gates/oracles


- title: Quantum Protocols and Quantum Algorithms
  url: /ch-algorithms
  sections:
    - title: Defining Quantum Circuits
      id: quantum-circuits
      uuid: d90cbfb6-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/defining-quantum-circuits
    - title: Deutsch-Jozsa Algorithm
      id: deutsch-jozsa-algorithm
      uuid: dc9d3aa2-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/deutsch-jozsa
    - title: Bernstein-Vazirani Algorithm
      id: bernstein-vazirani-algorithm
      uuid: df6e5a40-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/bernstein-vazirani
    - title: Simon's Algorithm
      id: simons-algorithm
      uuid: e2714126-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/simon
    - title: Quantum Fourier Transform
      id: quantum-fourier-transform
      uuid: e59ba472-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/quantum-fourier-transform
    - title: Quantum Phase Estimation
      id: quantum-phase-estimation
      uuid: e8ac9ec8-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/quantum-phase-estimation
    - title: Shor's Algorithm
      id: shors-algorithm
      uuid: ec157cd8-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/shor
    - title: Grover's Algorithm
      id: grovers-algorithm
      uuid: eebb7488-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/grover
    - title: Quantum Counting
      id: quantum-counting
      uuid: f1a9942c-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/quantum-counting
    - title: Quantum Teleportation
      id: quantum-teleportation
      uuid: f4f4a090-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/teleportation
    - title: Superdense Coding
      id: superdense-coding
      uuid: f87cbd42-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/superdense-coding
    - title: Quantum Key Distribution
      id: quantum-key-distribution
      uuid: fbafa8c6-b519-11ec-b909-0242ac120002
      url: /ch-algorithms/quantum-key-distribution
    - title: The Hidden Shift Problem
      id: hidden-shift-problem
      uuid: 56d13a0c-cae7-11ec-9d64-0242ac120002
      url: /ch-algorithms/hidden-shift-problem


- title: Quantum Algorithms for Applications
  url: /ch-applications
  sections:
    - title: Solving Linear Systems of Equations using HHL
      id: solving-linear-systems-of-equations-using-hhl-and-its-qiskit-implementation
      uuid: 01484810-b51a-11ec-b909-0242ac120002
      url: /ch-applications/hhl_tutorial
    - title: Simulating Molecules using VQE
      id: simulating-molecules-using-vqe
      uuid: 041df288-b51a-11ec-b909-0242ac120002
      url: /ch-applications/vqe-molecules
    - title: Solving combinatorial optimization problems using QAOA
      id: solving-combinatorial-optimization-problems-using-qaoa
      uuid: 06ff7ada-b51a-11ec-b909-0242ac120002
      url: /ch-applications/qaoa
    - title: Solving Satisfiability Problems using Grover's Algorithm
      id: solving-satisfiability-problems-using-grovers-algorithm
      uuid: 09d1529c-b51a-11ec-b909-0242ac120002
      url: /ch-applications/satisfiability-grover
    - title: Hybrid quantum-classical Neural Networks with PyTorch and Qiskit
      id: hybrid-quantum-classical-neural-networks-with-pytorch-and-qiskit
      uuid: 0cac4d14-b51a-11ec-b909-0242ac120002
      url: /ch-machine-learning/machine-learning-qiskit-pytorch
    - title: Variational Quantum Linear Solver
      id: the-variational-quantum-linear-solver
      uuid: 1163f456-b51a-11ec-b909-0242ac120002
      url: /ch-paper-implementations/vqls
    - title: Quantum Image Processing - FRQI and NEQR Image Representations
      id: flexible-representation-of-quantum-images-frqi
      uuid: 14acf6a8-b51a-11ec-b909-0242ac120002
      url: /ch-applications/image-processing-frqi-neqr
    - title: Facial Expression Recognition
      id: facial-expression-recognition
      uuid: 22cb8bf2-cae9-11ec-9d64-0242ac120002
      url: /ch-applications/facial-expression-recognition
    - title: Quantum Edge Detection
      id: quantum-edge-detection
      uuid: 3e202caa-cae9-11ec-9d64-0242ac120002
      url: /ch-applications/quantum-edge-detection
    - title: Travelling Salesman Problem
      id: tsp
      uuid: 443c52b2-cae9-11ec-9d64-0242ac120002
      url: /ch-paper-implementations/tsp


- title: Investigating Quantum Hardware Using Quantum Circuits
  url: /quantum-hardware
  sections:
    - title: Introduction to Quantum Error Correction using Repetition Codes
      id: introduction-to-quantum-error-correction-via-the-repetition-code
      uuid: 197f7f66-b51a-11ec-b909-0242ac120002
      url: /quantum-hardware/error-correction-repetition-code
    - title: Measurement Error Mitigation
      id: measurement-error-mitigation
      uuid: 1c5bd31a-b51a-11ec-b909-0242ac120002
      url: /quantum-hardware/measurement-error-mitigation
    - title: Randomized Benchmarking
      id: randomized-benchmarking
      uuid: 1fa1d22c-b51a-11ec-b909-0242ac120002
      url: /quantum-hardware/randomized-benchmarking
    - title: Measuring Quantum Volume
      id: measuring-quantum-volume
      uuid: 22ab0bd2-b51a-11ec-b909-0242ac120002
      url: /quantum-hardware/measuring-quantum-volume
    - title: The Density Matrix and Mixed States
      id: density-matrix
      uuid: 498dce44-cae9-11ec-9d64-0242ac120002
      url: /quantum-hardware/density-matrix


- title: Investigating Quantum Hardware Using Microwave Pulses
  url: /quantum-hardware-pulses
  sections:
    - title: Calibrating Qubits with Qiskit Pulse
      id: calibrating-qubits-using-qiskit-pulse
      uuid: 292100ca-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/calibrating-qubits-pulse
    - title: Accessing Higher Energy States
      id: accessing-higher-energy-states-with-qiskit-pulse
      uuid: 2bf0d316-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/accessing_higher_energy_states
    - title: Introduction to Transmon Physics
      id: introduction-to-transmon-physics
      uuid: 2e944e0e-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/transmon-physics
    - title: Circuit Quantum Electrodynamics
      id: circuit-quantum-electrodynamics
      uuid: 31b2ccdc-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/cQED-JC-SW
    - title: Exploring the Jaynes-Cummings Hamiltonian with Qiskit Pulse
      id: exploring-the-jaynes-cummings-hamiltonian-with-qiskit-pulse
      uuid: 346d7eea-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/Jaynes-Cummings-model
    - title: Measuring the Qubit ac-Stark Shift
      id: measuring-the-qubit-ac-stark-shift
      uuid: 37110d92-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/ac-Stark-shift
    - title: Hamiltonian Tomography
      id: hamiltonian-tomography
      uuid: 3a440960-b51a-11ec-b909-0242ac120002
      url: /ch-quantum-hardware/hamiltonian-tomography


- title: Quantum Computing Labs
  url: /ch-labs
  sections:
    - title: Lab 1. Quantum Circuits
      id: lab-1-quantum-circuits
      uuid: 3ff5a7ec-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab01_QuantumCircuits
    - title: Lab 2. Single Qubit Gates
      id: lab-2-single-qubit-gates
      uuid: 43418a88-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab02_Single_Qubit_Gates
    - title: Lab 3. Quantum Measurement
      id: lab-3-quantum-measurements
      uuid: 45aa5412-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab03_QuantumMeasurement
    - title: Lab 4. Bell Circuit & GHZ Circuit
      id: lab-4-bell-ghz-circuit
      uuid: 4a04a0f8-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab04_Bell_GHZ_Circuit
    - title: Lab 5. Accuracy of Quantum Phase Estimation
      id: lab-5-accuracy-of-quantum-phase-estimation
      uuid: 4ca77b5a-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab05_AccuracyQPE
    - title: Lab 6. Iterative Quantum Phase Estimation
      id: lab-6-iterative-phase-estimation-algorithm
      uuid: 502f02fc-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab06_IterativePhaseEstimation
    - title: Lab 7. Scalable Shor’s Algorithm
      id: lab-7-scalable-shors-algorithm
      uuid: 535b2b18-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab07_Scalable_Shor_Algorithm
    - title: Lab 8. Grover's search with an unknown number of solutions
      id: lab-8-grovers-search-with-an-unknown-number-of-solutions
      uuid: 571376ac-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab08_Grover_search_with_an_unknown_number_of_solutions
    - title: Lab 9. Quantum Simulation as a Search Algorithm
      id: lab-9-quantum-simulation-as-a-search-algorithm
      uuid: 59a076f4-b51a-11ec-b909-0242ac120002
      url: /ch-labs/Lab09_QuantumSimulationSearchAlgorithm


- title: Appendix
  url: /ch-appendix
  sections:
    - title: Linear Algebra
      id: an-introduction-to-linear-algebra-for-quantum-computing
      uuid: 5d2bb2ca-b51a-11ec-b909-0242ac120002
      url: /ch-appendix/linear_algebra
    - title: Qiskit
      id: basic-qiskit-syntax
      uuid: 5fd6b79a-b51a-11ec-b909-0242ac120002
      url: /ch-appendix/qiskit


- title: Games and Demos
  url: /ch-demos
  sections:
    - title: Hello Qiskit Game
      id: bonus-level-sandbox
      uuid: 63a85f0e-b51a-11ec-b909-0242ac120002
      url: /ch-ex/hello-qiskit
    - title: Estimating Pi Using Quantum Phase Estimation Algorithm
      id: estimating-pi-pi-using-quantum-phase-estimation-algorithm
      uuid: 69b9707c-b51a-11ec-b909-0242ac120002
      url: /ch-demos/piday-code
    - title: Local Reality and the CHSH Inequality
      id: local-reality-and-the-chsh-inequality
      uuid: 6c507826-b51a-11ec-b909-0242ac120002
      url: /ch-demos/chsh
    - title: Interactivity Index
      id: widgets-demonstration
      uuid: 6f1f26ce-b51a-11ec-b909-0242ac120002
      url: /ch-demos/widgets-index
    - title: Quantum Coin Game
      id: coin-game
      uuid: 4e72eec6-cae9-11ec-9d64-0242ac120002
      url: /ch-demos/coin-game
    - title: First Quantum Game
      id: first-quantum-game
      uuid: 53a49e62-cae9-11ec-9d64-0242ac120002
      url: /ch-demos/first-quantum-game
    - title: Variational Quantum Regression
      id: variational-quantum-regression
      uuid: 57d7e37c-cae9-11ec-9d64-0242ac120002
      url: /ch-demos/variational-quantum-regression


- title: Problem Sets
  url: /problem-sets
  sections:
    - title: Single Systems Problem Set
      id: single_systems_problem_set
      uuid: e4f72595-1e9e-47fd-8780-345360b53fef
      url: /problem-sets/single_systems_problem_set
    - title: Quantum Enigma Problem Set
      id: quantum_enigma_problem_set
      uuid: e4f72595-1e9e-47fd-8780-345360b53fef
      url: /problem-sets/quantum_enigma_problem_set


- title: Examples
  url: /examples
  type: docs
  sections:
    - title: Annotations
      id: annotations
      uuid: 745440a2-b51a-11ec-b909-0242ac120002
      url: /examples/annotations
    - title: Blocks
      id: blocks
      uuid: 771a4f16-b51a-11ec-b909-0242ac120002
      url: /examples/blocks
    - title: Widgets
      id: widgets
      uuid: 79da872a-b51a-11ec-b909-0242ac120002
      url: /examples/widgets
    - title: Grader
      id: grader
      uuid: 5e7e52f6-437d-4edf-be7b-89d38f96007d
      url: /examples/grader
    - title: Locale
      id: locale
      uuid: 7cbf7978-b51a-11ec-b909-0242ac120002
      url: /examples/locale


- title: Quantum Algorithms
  url: /algorithms
  type: learning-path
  sections:
    - title: Phase Kickback
      id: phase-kickback
      uuid: 976e9da6-6c33-4e2f-b7eb-f9588f700f07
      url: /algorithms/phase-kickback


- title: Introduction to Quantum Computing
  url: /introduction
  type: learning-path
  sections:
    - title: Why quantum computing?
      uuid: bdb1d662-e0f6-428a-8830-befe6b47f320
      id: why-quantum-computing
      url: /intro/why-quantum-computing
    - title: The atoms of computation
      id: the-atoms-of-computation
      uuid: 37ef477e-ab8d-11ec-b909-0242ac120002
      url: /intro/atoms-of-computation
    - title: What is quantum?
      id: what-is-quantum
      uuid: 7c765036-aebc-11ec-b909-0242ac120002
      url: /intro/what-is-quantum
    - title: Describing quantum computers
      id: describing-quantum-computers
      uuid: 9260a554-aebc-11ec-b909-0242ac120002
      url: /intro/describing-quantum-computers
    - title: Entangled states
      id: entangled-states
      uuid: 98aa9032-aebc-11ec-b909-0242ac120002
      url: /intro/entangled-states
    - title: Visualizing entanglement
      id: visualizing-entanglement
      uuid: 9e8ceb9e-aebc-11ec-b909-0242ac120002
      url: /intro/visualizing-entanglement
    - title: Grovers algorithm
      id: grovers-search-algorithm
      uuid: a2e6f7a2-aebc-11ec-b909-0242ac120002
      url: /intro/grover-intro
    - title: Project
      id: project
      uuid: e25c3f90-aebd-11ec-b909-0242ac120002
      url: /intro/project


- title: Summer School 2020
  url: /2020
  type: learning-path
  sections:
    - title: Qubits and Quantum States, Quantum Circuits, Measurements
      id: qubits-states-circuits-measurements
      uuid: a45b8936-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-00
    - title: Writing and Running Quantum Programs
      id: writing-running-programs
      uuid: a7412732-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-01
    - title: Shor's Algorithm I Quantum Fourier Transform, Quantum Phase Estimation
      id: shors-algorithm-i-fourier-transform-phase-estimation
      uuid: aaedcbb0-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-02
    - title: Shor's Algorithm II From Factoring to Period-Finding, Writing the Quantum Program
      id: shors-algorithm-ii-from-factoring-to-period-finding-writing-program
      uuid: ada10d7c-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-03
    - title: Quantum Error Correction using Repetition Codes
      id: error-correction-using-repetition-codes
      uuid: b10b5bf2-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-04
    - title: Superconducting Qubits I Quantizing a Harmonic Oscillator, Josephson Junctions
      id: superconducting-qubits-i-quantizingharmonic-oscillator-josephson-junctions
      uuid: b3e1bc18-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-05
    - title: Superconducting Qubits II Circuit Quantum Electrodynamics, Readout and Calibration Methods
      id: superconducting-qubits-ii-circuit-electrodynamics-readout-calibration-methods
      uuid: b6bc1442-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-06
    - title: Quantum Chemistry I Obtaining the Qubit Hamiltonian for H2 and LiH
      id: chemistry-i-obtaining-qubit-hamiltonian-h2-lih
      uuid: b95d099a-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-07
    - title: Quantum Chemistry II Finding the Ground States of H2 and LiH
      id: chemistry-ii-finding-ground-states-h2-lih
      uuid: bc25a4c0-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-08
    - title: Careers in Quantum Computin
      id: careers-in-computing
      uuid: bf1b8a5a-b51a-11ec-b909-0242ac120002
      url: /summer-school/2020/lec-09


- title: Summer School 2021
  url: /2021
  type: learning-path
  sections:
    - title: Vector Spaces, Tensor Products, and Qubits
      id: lec1-1-vector-spaces-tensor-products-qubits
      uuid: c2ebedbe-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec1.1
    - title: Introduction to Quantum Circuits
      id: lec1-2-introduction-quantum-circuits
      uuid: c5fb76be-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec1.2
    - title: Simple Quantum Algorithms I
      id: lec2-1-simple-quantum-algorithms-i
      uuid: c8a7b51c-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec2.1
    - title: Simple Quantum Algorithms II
      id: lec2-2-simple-quantum-algorithms-ii
      uuid: cb3c1764-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec2.2
    - title: Noise in Quantum Computers pt 1
      id: lec3-1-noise-quantum-computers-1
      uuid: cec0e98c-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec3.1
    - title: Noise in Quantum Computers pt 2
      id: lec3-2-noise-quantum-computers-pt-2
      uuid: d1c81efc-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec3.2
    - title: Lab 1
      id: lab1-quantum-computing-algorithm-operations
      uuid: d42ae134-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lab1
    - title: Introduction to Classical Machine Learning
      id: lec4-1-introduction-classical-machine-learning
      uuid: e0df92f8-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec4.1
    - title: Advanced Classical Machine Learning
      id: lec4-2-advanced-classical-machine-learning
      uuid: e48de1b6-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec4.2
    - title: Building a Quantum Classifier
      id: lec5-1-building-quantum-classifier
      uuid: e73ed898-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec5.1
    - title: Introduction to the Quantum Approximate Optimization Algorithm and Applications
      id: lec5-2-introduction-quantum-approximate-optimization-algorithm-applications
      uuid: eb731028-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec5.2
    - title: Lab 2
      id: lab2-variational-algorithms
      uuid: ee521226-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lab2
    - title: From Variational Classifiers to Linear Classifiers
      id: lec6-1-from-variational-classifiers-linear-classifiers
      uuid: f1194114-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec6.1
    - title: Quantum Feature Spaces and Kernels
      id: lec6-2-quantum-feature-spaces-kernels
      uuid: f5365020-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec6.2
    - title: Quantum Kernels in Practice
      id: lec7-1-quantum-kernels-practice
      uuid: f81eb3cc-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec7.1
    - title: Lab 3
      id: lab3-introduction-quantum-kernels-support-vector-machines
      uuid: fb8983ca-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lab3
    - title: Introduction and Applications of Quantum Models
      id: lec8-1-introduction-applications-quantum-models
      uuid: fe54b430-b51a-11ec-b909-0242ac120002
      url: /summer-school/2021/lec8.1
    - title: Barren Plateaus, Trainability Issues, and How to Avoid Them
      id: lec8-2-barren-plateaus-trainability-issues-how-avoid-them
      uuid: 025748fe-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lec8.2
    - title: Lab 4
      id: lab4-introduction-training-quantum-circuits
      uuid: 05245a54-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lab4
    - title: Introduction to Quantum Hardware
      id: lec9-1-introduction-quantum-hardware
      uuid: 07b79f1a-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lec9.1
    - title: Hardware Efficient Ansatze for Quantum Machine Learning
      id: lec9-2-hardware-efficient-ansatze-quantum-machine-learning
      uuid: 0a70ba52-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lec9.2
    - title: Lab 5
      id: lab5-introduction-hardware-efficient-ansatze-quantum-machine-learning
      uuid: 0d5b854e-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lab5
    - title: Advanced QML Algorithms
      id: lec10-1-advanced-qml-algorithms
      uuid: 100e0ee2-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lec10.1
    - title: The Capacity and Power of Quantum Machine Learning Models & the Future of Quantum Machine Learning
      id: lec10-2-the-capacity-power-quantum-machine-learning-models-future-quantum-machine-learning
      uuid: 12c23f78-b51b-11ec-b909-0242ac120002
      url: /summer-school/2021/lec10.2

- title: Summer School 2022
  url: /2022
  type: learning-path
  sections:
    - title: History of Quantum Computing and Motivation for Quantum Simulation
      id: history-quantum-computing-motivation-quantum-simulation
      uuid: 820caba4-2784-419f-badb-038632a8d4bd
      url: /summer-school/2022/lec-1
    - title: Introduction to Linear Algebra, Prerequisite Mathematics, and Circuit Composition
      id: introduction-linear-algebra-prerequisite-mathematics-circuit-composition
      uuid: 6e908f0d-f6c3-4a96-8b6e-d0c355aa0fd0
      url: /summer-school/2022/lec-2
    - title: Lab 1
      id: lab-1
      uuid: 6b9733a9-c37d-416a-a21d-79666f6c6e4f
      url: /summer-school/2022/lab-1
    - title: Hamiltonian Time Evolution
      id: hamiltonian-time-evolution
      uuid: 40898326-7668-4076-b671-01d76c914f2d
      url: /summer-school/2022/lec-3
    - title: Simulation Problems
      id: simulation-problems
      uuid: 3f1b1d6a-1d9f-48dc-b202-f9f027ad9f94
      url: /summer-school/2022/lec-4
    - title: Lab 2
      id: lab-2
      uuid: 12c18054-d8f9-4347-bb82-3f8887f9a89b
      url: /summer-school/2022/lab-2
    - title: Noisy Real Hardware, Noise in Quantum Computers
      id: noisy-real-hardware-noise-quantum-computers
      uuid: ada6cc30-bfdf-4fcf-95c3-3377647ca6c1
      url: /summer-school/2022/lec-5
    - title: Broad Overview of Quantum Chemistry Simulation and Why it is a Challenge
      id: broad-overview-quantum-chemistry-simulation-why-is-challenge
      uuid: 0eb99b15-a8e2-4472-8dfe-44d3172d7819
      url: /summer-school/2022/lec-6
    - title: Lab 3
      id: lab-3
      uuid: f310e2c1-6216-40c7-92c5-f6e86a665130
      url: /summer-school/2022/lab-3
    - title: Methods for Quantum Simulation
      id: methods-quantum-simulation
      uuid: 945603e2-5538-451a-89f5-e5fd273c80d1
      url: /summer-school/2022/lec-7
    - title: Quantum Static Simulation
      id: quantum-static-simulation
      uuid: a058a165-6716-4f75-b228-9ed003bba2a7
      url: /summer-school/2022/lec-8
    - title: Lab 4
      id: lab-4
      uuid: 21bee5f4-f7ee-49cb-99b7-4eb950dedf38
      url: /summer-school/2022/lab-4
    - title: Quantum Dynamics
      id: quantum-dynamics
      uuid: 19bc4a81-07e8-4397-befd-76aa973d2c8c
      url: /summer-school/2022/lec-9


- title: Quantum Machine Learning
  url: /machine-learning
  type: learning-path
  sections:
    - title: Introduction
      id: introduction
      uuid: 16e935fc-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/introduction
    - title: Parametrized quantum circuits
      id: parameterized-quantum-circuits
      uuid: 19a9f4de-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/pqc
    - title: Data encoding
      id: data-encoding
      uuid: 1d09af66-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/encoding
    - title: Training quantum circuits
      id: training-quantum-circuits
      uuid: 1fb38444-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/training
    - title: Supervised learning
      id: supervised-learning
      uuid: 22cf51bc-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/supervised
    - title: Variational classification
      id: variational-classification
      uuid: 26951034-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/vqc
    - title: Quantum feature maps and kernels
      id: quantum-feature-maps-kernels
      uuid: 29b0fda0-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/kernel
    - title: Unsupervised learning
      id: unsupervised-learning
      uuid: 2cc6b386-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/unsupervised
    - title: Quantum generative adversarial networks
      id: quantum-generative-adversarial-networks
      uuid: 2ff2a3e4-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/qgan
    - title: Project
      id: project
      uuid: 345f0c2e-b51b-11ec-b909-0242ac120002
      url: /quantum-machine-learning/project