Mathematical concepts and conventions

Internal data representation of Quantumsim uses superoperator formalism 1 2. We store states as vectors in Hilbert-Schmidt space of dimension \(d^2\), where \(d = \sum_{i=1}^{N} d_i\) is a sum of dimensionalities of all qudits in a system. This is done by expanding density matrix and quantum operations in a basis of Hermitian matrices (see Pauli Bases). In this representation, quantum state \(\rho\) is a real-valued vector, and quantum operation is a real-valued matrix.

• Pauli Bases
  • Orthonormality condition
  • Common bases
  • State representation in Quantumsim
• Pauli Transfer Matrix Manipulation
  • Conversion between Kraus and PTM representations
• Lindblad equation

1

A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, “Classical and Quantum Computation” (American Mathematical Society, 2002).

2

D. Greenbaum, “Introduction to Quantum Gate Set tomography”, arXiv:1509.02921.