Practical Quantum Computing for Scientists

Quantum computers are here, the next big challenge: A quantum skills shortage. The quantum computing industry will be a $65 billion market by 2030; others anticipate that up to 20% of organizations could be budgeting for quantum computing in 2023, up from 1% in 2018.

Gartner

Why will you need Quantum computing as a scientist?

Our current understanding of nature is quantum mechanical; therefore, it is natural to argue that science should use the power of quantum computers to understand Nature. This lecture aims to introduce science students with practical, hands-on, current skills working with commercial quantum computers and quantum simulators in a scientific context. The course will introduce topics such as Quantum Circuit diagrams, Complexity theory, “The Canon” algorithms, Quantum Fourier transform,  Hamiltonian Simulation, Common error channels, Fault-Tolerant Quantum Computation, Quantum Machine Learning, and other paradigms in Quantum computing such as bosonic sampling.

Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.

Richard Feynman "Simulating Physics with Computers", International Journal of Theoretical Physics, volume 21, 1982, p. 467-488, at p. 486 (final words)

Course content

 

Chapter 1: Review & Mathematical Foundations

  • Linear Algebra
  • Review of the four postulates of quantum mechanics
    • Postulate 1: Individual quantum systems
    • Postulate 2: Quantum operations
    • Postulate 3: Composite quantum systems
    • Postulate 4: Measurement
  • No cloning theorem
  • Quantum entanglement
  • Density matrices
    • The partial trace operation
    • Using partial trace to detect entanglement
    • How the postulates of quantum mechanics apply to density operators

Chapter 2: Quantum Circuit Diagrams

  • Quantum Circuit Diagrams
  • Quantum operators
    • Unary
    • Binary
    • Ternary
    • Comparison with classical gates
  • The universality of Quantum operators
  • The Bloch Sphere 

Chapter 3: Complexity Theory; Entropy and Entanglement Distillation

  • Complexity Theory
    • Time Complexity
    • Complexity Classes
  • Entropy
    • Shannon entropy
    • Von Neumann Entropy
  • Quantifying entanglement in composite quantum systems
  • Entanglement distillation

Chapter 4: The Deutsch-Josza and Berstein-Vazirani algorithms

  • Functions as oracles
  • The problem: Is f constant or balanced?
  • The algorithm
    • A naive idea
    • Deutsch’s algorithm
    • The phase kickback trick
    • The Deutsch-Josza algorithm
    • The Berstein-Vazirani algorithm

Chapter 5: Strategies of Input Encoding

  • Basis Encoding
  • Amplitude Encoding
  • Time-Evolution Encoding
  • Hamiltonian Encoding

 

Chapter 6: Simon’s algorithm and applications to cryptography

  • Simon’s algorithm
    • Birthdays and a naive classical algorithm
    • Simon’s algorithm
  • Application to cryptography

Chapter 7: The Quantum Fourier Transform

  • From Vandermonde matrices to the Discrete Fourier Transform
  • The Quantum Fourier Transform (QFT)
  • Quantum Phase Estimation (QPE)
  • Applications of QPE
  • Quantum algorithms for QPE

Chapter 8: Shor’s quantum factoring algorithm

  • The integer factorization problem
  • The factoring algorithm
    • Reducing FACTOR to order-finding
    • Sampling via QPE
    • Postprocessing via continued fractions
  • Application: Breaking RSA

Chapter 9: Noise

Chapter 10: CV algorithms

Chapter 11: Variational Circuits as Machine Learning Models (time permitting)

  • How to Interpret a Quantum Circuit as a Model
    • Deterministic Quantum Models
    • Probabilistic Quantum Models
    • An Example: Variational Quantum Classifier
    • An Example: Variational Generator
  • Which Functions Do Variational Quantum Models Express?
    • Quantum Models as Linear Combinations of Periodic Functions
    • An Example: The Pauli-Rotation Encoding
  • Training Variational Quantum Models
    • Gradients of Quantum Computations
    • Parameter-Shift Rules
    • Barren Plateaus
    • Generative Training
  •  Quantum Circuits and Neural Networks
    • Emulating Nonlinear Activations
    • Variational Circuits as Deep Linear Neural Networks
    • Time-Evolution Encoding as an Exponential Activation

Syllabus

 

Course Title

PHYS437 Practical Quantum Computing for Scientists

Lecturers

Barış Malcıoğlu

Grading

Midterm %20, Term project %40, Hands-on sessions & homework %40

Hands-On sessions

  • Attendance to all of the hands-on sessions, and submitting the assigned hands-on work is mandatory. Any missed hands-on session, or assigned hands-on work will result in N/A grade. Only officially documented cases (such as medical reports) will be considered for exemption.

Midterm Exam

  • The midterm exam will involve a theory part and a programming part.
  • The theory part should be answered using a Latex/Word processor, converted to pdf
  • The programming part must be an ASCII text file containing python code (*.py).
  • The files should be uploaded to supplied Turnitin interface. Any incompatible input will be disregarded.  

Term projects

  • The term project is the final exam.

  • Participants are expected to present a project involving Quantum Computation, Quantum Communication, or Quantum hardware.

  • The term project consists of these parts:
    • A 1-page abstract describing the project
    • Presentation (~20 minutes), Q&A session after the talk (~10 minutes)
    • (Optional) A final report
  • The presenter will be graded according to the scientific quality of the presentation

  • The audience will be graded according to their participation in the Q&A session.

  • The term projects will be presented in the last 3-4 weeks

  • Attendance to the term project presentations is mandatory. The first missed week will result in a reduction of your final grade to %65. The second missed week will result in a reduction of your final grade to %35. If you miss three weeks, you will receive N/A grade.

  • Only one missed week might be allowed with a valid official excuse.

Textbooks

Theory Content:

  • "Quantum Computing for the Quantum Curious" Ciaran Hughes, Joshua Isaacson, Anastasia Perry, Ranbel F. Sun, Jessica Turner https://doi.org/10.1007/978-3-030-61601-4 (open Access)
  • "Quantum Computing: Lecture Notes" Ronald de Wolf arXiv:1907.09415
  • "Introduction to Quantum Computation" Sevag Gharibian (Can be obtained from his course page here)

Lab Content:

Optional content (time permitting)

 

More material

Students are required to open an account in IBM Quantum Cloud