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.
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.
Course prerequisites
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.
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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.
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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:
- Qiskit Textbook
- Xanadu Quantum Codebook
- "Quantum Computing: An Applied Approach" Jack D. Hidary https://doi.org/10.1007/978-3-030-23922-0
Optional content (time permitting)
- "Lectures on Quantum Tensor Networks" Jacob Biamonte (for a systematic connection between circuit diagrams and CV systems)
- "Machine Learning with Quantum Computers" Maria Schuld, Francesco Petruccione https://doi.org/10.1007/978-3-030-83098-4
More
Students are required to open an account in IBM Quantum Cloud
