Phys 437

General information

• Syllabus
• Term Project Ideas

Theory sessions

Text

• Lecture 1 (Ch.1)
  • Jupyter
  • Markdown and LATEX
  • Anaconda
  • Exercise 1:
  • IBM Quantum Cloud
  • Some useful links
  • Introduction
    • Send it after class 1
    • Send it after class 2
    • Orthonormal bases
    • Send it after class 3
    • Linear maps.
    • Send it after class 4
    • Send it after class 5
• Lecture 2 (Ch.1)
  • The Image, Rank and Null space of a matrix
  • Send it after class 1
  • Answer
  • Matrix Operations
  • Send it after class 2
  • Answer
  • Outer products.
  • Eigenvalues and eigenvectors
  • Send it after class 3
  • Answer
  • Send it after class 4
  • Answer
  • The four postulates of Quantum Mechanics
    • Postulate 1: Individual Quantum systems
    • Send it after class 5
    • Answer
    • Postulate 2: Quantum operations
    • Send it after class 6
    • Answer
• Lecture 3 (Ch.1)
  • \(Z\) Gate
  • Hadamard Gate
  • Send it after class 1
    • Quantum Circuits
  • Send it after class 2
  • Postulate 3: Composite Quantum Systems
  • Send it after class 3
  • Send it after class 4
  • Send it after class 5
    • Quantum Entanglement
  • Send it after class 6
    • Two-qubit quantum gates.
  • Send it after class 7
• Lecture 4 (Ch.1)
  • Delayed choice quantum eraser
  • Postulate 4: Measurement
    • Send it after class 1
    • Projective Measurements.
    • Send it after class 3
  • Quantum Teleportation
    • Send it after class 4
• Lecture 5 (Ch.2)
  • No cloning theorem
    • Send it after class 1
  • Quantum entanglement
    • Bipartite entanglement
    • The Schmidt decomposition.
    • Send it after class 2
  • Density Matrices
    • Send it after class 3
    • The partial trace operation
    • Using partial trace to detect entanglement
    • How the postulates of quantum mechanics apply to density operators
• Lecture 6 (Ch.2)
  • Non-Local Games
  • Does entanglement allow superluminal signalling?
  • Non-local games
    • The CHSH game
    • Send it after class 1
    • Send it after class 2
  • The magic square game
    • Send it after class 3
    • Send it after class 4
    • Send it after class 5
    • Send it after class 6
• Lecture 7 (Ch.2)
  • Entropy and Entanglement Distillation
  • Entropy
    • Shannon entropy
    • Send it after class 3
    • Von Neumann Entropy
    • Send it after class 7
  • Quantifying entanglement in composite quantum systems
    • Send it after class 8
  • Entanglement distillation
    • Send it after class 9
• Lecture 8 (Ch.3)
  • Functions as oracles
  • The phase kickback trick
  • Grover search
    • The unstructured search problem
    • Grover’s algorithm
    • Send it after class 1
    • Send it after class 2
    • The start state \( \left|\psi\right\rangle \)
    • Send it after class 3
    • The goal.
    • Two reflections make a rotation.
    • Send it after class 4
    • The number of iterations required.
    • Send it after class 5
  • Approximate counting
    • Intuition
    • Quantizing the basic idea.
    • Grover’s algorithm
    • Send it after class 1
    • Send it after class 2
    • The start state \( \left|\psi\right\rangle \)
    • Send it after class 3
    • The goal.
    • Two reflections make a rotation.
    • Send it after class 4
    • The number of iterations required.
    • Send it after class 5
  • Approximate counting
    • Intuition
    • Quantizing the basic idea.

Online material

• Lecture 1 online material
• Lecture 2 online material
• Lecture 3 online material
  • Session Recording
• Lecture 4 online material
  • Session Recording
• Lecture 5 online material
• Lecture 6 online material
• Lecture 7 online material

Hands-on sessions

Pre-compiled Jupyter

• Hands-on 1
  • Preliminary
  • Exploring Qubits with Qiskit
  • The Rules of Measurement
    • Normalisation
    • In class exercise
    • Alternative measurement
    • Global Phase
    • A Note about Quantum Simulators
  • The Bloch Sphere
  • In Class Exercise
  • Your first multi-qubit quantum circuit
    • What’s a method?
    • Basics of encoding an input
• Hands-on 2
  • Representing Multi-Qubit States
  • Single Qubit Gates on Multi-Qubit Statevectors
    • Send it after class 1
  • Multi-Qubit Gates
    • The CNOT-Gate
    • Entangled States
    • Visualizing Entangled States
    • Send it after class 2
  • Exploring the CNOT-Gate
  • Phase Kickback
    • Explaining the CNOT Circuit Identity
    • Kickback with the T-gate
    • Send it after class 3:
• Hands-on 3
  • Single Qubit Gates
    • Contents
    • 1. The Pauli Gates
    • 2. Digression: The X, Y & Z-Bases
    • 3. The Hadamard Gate
    • 4. Digression: Measuring in Different Bases
    • 5. The P-gate
    • 6. The I, S and T-gates
    • 7. The U-gate
  • Quantum Measurements
    • Part 1: Measuring the state of a qubit
    • Part 2: Measuring Energy
    • Part 3: Execute the circuits on Quantum Computer
• Hands-on 4
  • Using your IBM credentials locally
  • Qiskit Visualization tools
    • Plot a state
    • Simulators
  • 2. Introduction to Quantum Gates and Circuits. Building Circuits with multiple components.
    • Quantum Circuit Properties
    • Final Statevector and Unitary
    • Other components
  • 3. Run on real hardware. Compiling Circuits
    • Optimization level
  • Send it after class
• Hands-on 5
  • Quantum Coin Game
    • What are the rules of this game ?
    • Analogy
    • Approach
    • Optimal Strategy
    • Lets play this version using Qiskit
    • Conclusion
    • Send it after class 1:
  • Local Reality and the CHSH inequality
    • The CHSH inequality
    • Send it after class 2
• Hands-on 6
  • Entanglement Purification: The BBPSSW Protocol
  • Part I: Introduction to Entanglement Purification and the BBPSSW Protocol
    • 1.1 Concept
    • 1.2 Quantum Protocol
  • Part II: Implementation of Quantum Circuit for BBPSSW Protocol in Qiskit
    • 2.1 Basic Code Imports
    • 2.2 Definitions
    • 2.3 Quantum Register and Quantum Circuit
    • 2.4 (Conditional) Quantum State Tomography
  • Part III: Simulation of the BBPSSW Protocol using Qiskit
    • 3.1 Single Quantum System
    • 3.2 Ensemble Average
  • Part IV: Including Noise in the Simulation Model
    • 4.1 IBM Q Account
    • 4.2 Creation of Noise Model in Qiskit
    • 4.3 Simulation Including Noise
  • Part V: Entanglement Purification on a Real IBM Q Device
    • 5.1 IBM Q Experience
    • 5.2 Initial State and Initial Fidelity
    • 5.3 Execution of the BBPSSW Protocol on a Real Device
  • Part VI: Conclusion and Further Ideas
  • References
• Hands-on 7
  • Grover’s Algorithm and Amplitude Amplification
    • Grover’s algorithm
    • Using the different types of classes as the oracle of Grover
    • Amplitude amplification
    • Dive into other arguments of Grover
  • Grover’s algorithm examples
    • Finding solutions to 3-SAT problems
  • Boolean Logical Expressions
  • Quantum Amplitude Estimation
    • Qiskit’s Amplitude Estimation workflow
    • Canonical AE
    • Iterative Amplitude Estimation
    • Maximum Likelihood Amplitude Estimation
    • Faster Amplitude Estimation
    • References
  • Send it after class
• Hands-on 8
  • Portfolio Diversification
    • Introduction
    • The Model
    • A Hybrid Approach
    • References
    • The Implementation
  • Classical solution using IBM ILOG CPLEX
  • Quantum Computing with IBM Q
    • Step 1
    • Step 2
    • Step 3
    • Step 4
    • Step 5
  • One qubit QARBM
  • Do it yourself

Online material

• Hands-on 1
• Hands-on 2
• Hands-on 3
• Hands-on 4
• Hands-on 5
• Hands-on 6
• Hands-on 7
• Hands-on 8
• Hands-on 9