Matrix

A general-purpose complex-valued matrix class used internally by quantum state and channel representations. Matrix wraps an underlying complex matrix and provides basic linear-algebra operations.

Signature

Matrix(data: numpy.ndarray)

Constructors

Default constructor

Matrix()

Constructs an empty Matrix object.

From data

Matrix(data: numpy.ndarray)

Constructs a Matrix from a 2-D complex numpy array (or an Eigen matrix).

Parameter	Type	Description
data	numpy.ndarray	A 2-D array of complex numbers.

Methods

ndarray

ndarray() -> numpy.ndarray

Return the internal matrix data as a numpy.ndarray.

row_total

row_total() -> int

Return the number of rows in the matrix.

col_total

col_total() -> int

Return the number of columns in the matrix.

is_hermitian

is_hermitian() -> bool

Return True if the matrix is Hermitian, i.e., $A=A^{†}$.

transpose

transpose() -> Matrix

Return the transpose of the matrix, $A^T$.

T

T() -> Matrix

Alias for transpose(). Return the transpose of the matrix.

hermitian_conjugate

hermitian_conjugate() -> Matrix

Return the conjugate transpose (Hermitian adjoint) of the matrix, $A^{†}$.

adjoint

adjoint() -> Matrix

Alias for hermitian_conjugate(). Return the conjugate transpose of the matrix.

L2

L2() -> float

Return the L2 (Frobenius) norm of the matrix:

$$|A{|}_F=\sqrt{\sum _{i,j}|a_{ij}{|}^2}$$

at

at(rowIdx: int, colIdx: int) -> complex

Return the element at the specified row and column index.

Parameter	Type	Description
rowIdx	int	Row index (0-based).
colIdx	int	Column index (0-based).

Operators

Equality

matrix_a == matrix_b -> bool

Return True if the two matrices have identical internal data.

Examples

import numpy as np
from pyqpanda3.quantum_info import Matrix

# Construct from a numpy array
data = np.array([[1+0j, 0+1j],
                 [0-1j, 1+0j]])
m = Matrix(data)

print(m.row_total())      # 2
print(m.col_total())      # 2
print(m.is_hermitian())   # True

# Transpose and adjoint
mt = m.transpose()
ma = m.adjoint()

# Access a single element
val = m.at(0, 1)  # 0+1j

# Get the underlying numpy array
arr = m.ndarray()

See Also

• StateVector
• DensityMatrix
• Unitary