192.036 Introduction to Quantum Computing

Contents

1. Mathematical and Quantum Mechanical Preliminaries:
   • Complex Number
     • Imaginary Unit
     • Complex Modulus
     • Complex-Valued Function
   • Hilbert Space
   • L2 Space
     • Square-Integrable Function
   • Norm
   • Cauchy Sequence
   • Convergent Sequence
   • Limit
   • Banach Space
   • Inner Product
   • Inner Product Space
   • Orthonormal Basis
   • Linear Operator
   • Adjoint Operator
   • Hermitian Operator
   • Unitary Operator
   • Orthogonal Projection
   • Idempotent Operator
   • Eigenvector
   • Tensor Product
   • Bra-Ket Notation
   • Spectral Representation
   • Operator
   • Expected Value

Exercise Sheets

• Exercise Sheet 1