Chapter 1: Fundamentals of Quantum Information

In Chapter 1, you will learn quantum mechanics, which is necessary to fully understand how quantum computers work, and how to describe the states and operations of quantum computers. In particular, the idea of tensor products is essential for deep understanding of quantum computers. Although the computation of tensor products is a bit complicated, the Python math library SymPy supports algebraic processing of quantum mechanics, including tensor products. Let’s learn the basics of quantum mechanics and quantum computers while looking at the results of calculations using SymPy.

• 1-1. Qubit Representation
  • Meaning of complex probability amplitude
  • Representing quantum bit with Sympy
• 1-2. Qubit Operations
  • An example of one quantum bit operation: Pauli Operators
  • One quantum bit operation with SymPy
  • Column：Bra-ket notation
• 1-3. Multiqubit representation
  • Example：2 quantum bits case
  • Calculating Tensor Products
  • Tensor product calculation using SymPy
  • Tensor product of operators
  • Tensor product of operators using SymPy
  • When only a part of multiple qubits are measured
• Column: What is a universal gate set?
  • 【Note for those who want to know more details】
    • ◆ Decomposition of \(n\)-qubit unitary operations
    • ◆ Composition of 1-qubit unitary operations
• 1-4. Quantum Circuit Diagram