ECE 792-066 / CSC 791-025 Quantum Algorithms for Physical Sciences

Instructor: Yuan Liu (q_yuanliu@ncsu.edu)

Time and Location: Monday and Wednesday 3-4:15 pm, 1220 EB2. The course is hosted on Moodle. Recorded lectures can be accessed on Panopto.

Office hours: Thurs, 4-5 pm on Zoom

Objective or Description: This course will introduce advanced topics of modern quantum algorithms and their applications in sciences and engineering including quantum chemistry, many-body physics, and classical mechanics. The goal is to help students develop intuition and skills to design new quantum algorithms for novel applications in the future. Both near-term and fault-tolerant quantum algorithms will be discussed although the course will focus more on fault-tolerant algorithms with provable speedups. A brief discussion on quantum algorithms based on continuous-variable systems (such as bosonic modes instead of qubits) will be presented toward the end of the course. As a special topic course, contents of the course will be drawn from recent literature. By the end of the course, students will develop a broad picture of the landscape of quantum algorithms research and how they can be used to solve important problems in physical sciences. Students will also learn how to quantify and analyze quantum algorithm complexity. Light hands-on numerical programming exercises will be given to ensure best understanding of the course materials.

Prerequisites: Linear algebra (e.g., MA 305 or MA 405) and probability (e.g., ST 371) is required. Introductory courses on quantum computing (e.g., CSC 591-001/ECE 592-081, or ECE 592-100/ECE 492-054, or MA 591).

Textbook and references: Course materials will be compiled from different sources including recent literature. Written lecture notes will be uploaded to Moodle after each lecture. Some useful reference books are:

  • For a textbook on quantum information science, see Quantum Computation and Quantum Information by Nielsen and Chuang. Another source on the topic is Classical and Quantum Computation by Kitaev, Shen, and Vyalyi.
  • For an introduction to quantum chemistry, see Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund.
  • For an introduction to quantum mechanics, see Introduction to Quantum Mechanics by Griffiths and Schroeter.
  • For an introduction to many-body physics, see Introduction to Many-Body Physics by Coleman.
  • Useful lecture notes: “Quantum Algorithms for Scientific Computation” by Lin (UC Berkeley).

Topics:

  • Introduction
    • Overview of quantum mechanics and computation
      • Review of quantum mechanics and quantum computation (L1)
      • Composite quantum systems, density operator, measurement and POVM (L2)
      • Assessment of quantum algorithm performance (L2)
    • Overview of Physical Sciences Simulation
      • Characteristics of physical sciences (L3)
      • Hamiltonians of quantum chemistry (L3)
      • Orbitals, Hartree product, wave functions of many-fermionic and -bosonic systems; (L4)
      • Second quantization and matrix elements; static versus dynamics problems (L5)
  • Heuristic Quantum Algorithms
    • Variational algorithms and Quantum Machine Learning
    • QAOA
  • Quantum Algorithms with Provable Speedups I
    • Amplitude Amplification
    • Phase Estimation
    • Harrow-Hassidim-Lloyd algorithm for linear system of equations
  • Quantum Algorithms with Provable Speedups II
    • Trotter and Product Formula
    • Linear Combination of Unitaries
    • Quantum Signal Processing (QSP) and Quantum Singular Value Transform (QSVT)
    • Quantum Walks
  • Applications to physical sciences
    • State Preparation: ground states, excited states, thermal states
    • Hamiltonian simulation
    • Solving Partial Differential Equations: power system dynamics, heat transport equation, fluid dynamics (optional)
  • Hybrid discrete-continuous-variable quantum algorithms
    • Introduction to continuous-variable systems and their physical realization
    • Notion of universal control and universal computation on hybrid CV-DV systems
    • Generalization of DV quantum algorithms to CV, QSP, Trotter, LCU
    • Examples and Applications of Hybrid CV-DV algorithms:
      • DV-CV state transfer
      • Quantum Fourier transform from a continuous oracle
      • Bosonic Hamiltonian simulation (optional)
  • Final project Due and Presentations