qcp.matrices package¶

Submodules¶

qcp.matrices.dense_matrix module¶

class qcp.matrices.dense_matrix.DenseMatrix(state: qcp.matrices.types.MATRIX)[source]¶

Bases: qcp.matrices.matrix.Matrix

Implementation of a Dense Matrix class, where each matrix entry is stored in memory, including entries of value zero.

__add__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Add the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to add to this one.
Returns: A new matrix where the elements are the addition of the current and applied matrix elements.
Return type: Matrix

__getitem__(i: int) → qcp.matrices.types.VECTOR[source]¶

Get the List representation of the row of index i.

Parameters: i (int) – The row index to get.
Returns: List representation of the row.
Return type: VECTOR

__init__(state: qcp.matrices.types.MATRIX)[source]¶

Initialise the dense matrix, using the given nested list as our matrix content

Parameters: state (MATRIX) – A nested list containing values for each entry in the matrix.

__len__() → int[source]¶

Return the horizontal size of the DenseMatrix.

Returns: The number of columns in the DenseMatrix
Return type: int

__mul__(other: Union[SCALARS, Matrix]) → Matrix[source]¶

Override of the behaviour of the * multiplication operator.

If the operator is applied using a scalar value to this matrix, the matrix elements are each scaled by this number and a new matrix is returned containing these scaled elements.

If a Matrix object is applied using the * operator, the dot product of the two matrices is calculated, with the current matrix being the first Matrix, and the applied one the second, as order matters for matrix multiplication.

Parameters: other (Union[SCALARS, Matrix]) – The object being applied to this matrix
Returns: A new matrix containing the calculated values as appropriate.
Return type: Matrix

__setitem__(i: int, v: qcp.matrices.types.VECTOR)[source]¶

Set the given row inplace to the new row values in the given list.

Parameters

i (int) – The row index to modify
v (VECTOR) – The list of values to set the row to

__str__() → str[source]¶

Create a string representation of the Matrix, with rows separated by newlines, and bounded by ‘[‘/’]’ characters.

Returns: A string representation of the matrix suitable for printing.
Return type: str

__sub__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Subtract the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to subtract from this one.
Returns: A new matrix where the elements are the subtraction of the current and applied matrix elements.
Return type: Matrix

_abc_impl = <_abc._abc_data object>¶

_dot(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Calculate the dot product between this Matrix, and another Matrix.

Parameters: other (Matrix) – The matrix to dot product with this one.
Returns: A new matrix that conforms to the rules of matrix dot producting.
Return type: Matrix

columns() → qcp.matrices.types.MATRIX[source]¶

The transpose of the matrix as a nested list

Returns: A nested list of the matrix values transposed, indexed by column/row.
Return type: MATRIX

conjugate() → qcp.matrices.dense_matrix.DenseMatrix[source]¶

Create a new qcp.matrices.dense_matrix.DenseMatrix where each value in the matrix is the complex conjugate of the current matrix values.

Returns: A DenseMatrix object of the same dimensions of the current matrix, with each value conjugated in place.
Return type: DenseMatrix

get_state() → qcp.matrices.types.MATRIX[source]¶

Return the matrix values as a nested list

Returns: A nested list of the matrix values indexed by row/column
Return type: MATRIX

static identity(n: int) → qcp.matrices.dense_matrix.DenseMatrix[source]¶

Create the identity matrix with the given dimensions

Parameters: n (int) – The matrix dimension
Returns: The identity matrix of given dimension
Return type: DenseMatrix

property num_columns: int¶

Return the number of columns in the DenseMatrix.

Returns: The number of columns.
Return type: int

property num_rows: int¶

Return the number of rows in the DenseMatrix.

Returns: The number of rows
Return type: int

rows() → qcp.matrices.types.MATRIX[source]¶

Equivalent to qcp.matrices.dense_matrix.DenseMatrix.get_state().

Returns: A nested list of the matrix values indexed by row/column
Return type: MATRIX

trace() → qcp.matrices.types.SCALARS[source]¶

Calculate the sum of the diagonal elements of the matrix

Returns: The sum of all diagonal elements, with type determined by the value types.
Return type: SCALARS

transpose() → qcp.matrices.dense_matrix.DenseMatrix[source]¶

Flips the matrix elements along the diagonal, and return a new qcp.matrices.dense_matrix.DenseMatrix containing these values.

Returns: The transpose of the current matrix.
Return type: DenseMatrix

property unitary: bool¶

Check if matrix is Unitary (can be shifted to gates.py)

Parameters: Matrix – input: n x n matrix
Returns: Whether the matrix is unitary
Return type: bool

static zeros(nrow: int, ncol: int = 1) → qcp.matrices.dense_matrix.DenseMatrix[source]¶

Create a DenseMatrix of given dimensions, where each value of the matrix is zero.

Parameters

nrow (int) – The row dimension of the DenseMatrix
ncol (int) – The (optional) column dimenion of the DenseMatrix defaults to 1, to be a column vector.

Returns

The matrix object of our given size.

Return type

DenseMatrix

qcp.matrices.matrix module¶

class qcp.matrices.matrix.Matrix(state: qcp.matrices.types.MATRIX)[source]¶

Bases: abc.ABC

Method stubs for an implementation of a matrix.

__add__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Add the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to add to this one.
Returns: A new matrix where the elements are the addition of the current and applied matrix elements.
Return type: Matrix

__getitem__(i: int) → qcp.matrices.types.VECTOR[source]¶

Return the row elements for the given row index in a list representation

Parameters: i (int) – The index of the row to get the elements of
Returns: A list containing the row elements
Return type: VECTOR

__init__(state: qcp.matrices.types.MATRIX)[source]¶

Initialise the Matrix object, setting the matrix elements based off of the given nested list, and inferring the matrix dimensions from the list dimensions

Parameters: state (MATRIX) – The nested list containing the matrix elements

__len__() → int[source]¶

Return the horizontal width of the matrix.

Returns: The width of the matrix
Return type: int

__mul__(other: Union[SCALARS, Matrix]) → Matrix[source]¶

Override of the behaviour of the * multiplication operator.

If the operator is applied using a scalar value to this matrix, the matrix elements are each scaled by this number and a new matrix is returned containing these scaled elements.

If a Matrix object is applied using the * operator, the dot product of the two matrices is calculated, with the current matrix being the first Matrix, and the applied one the second, as order matters for matrix multiplication.

Parameters: other (Union[SCALARS, Matrix]) – The object being applied to this matrix
Returns: A new matrix containing the calculated values as appropriate.
Return type: Matrix

__rmul__(s: qcp.matrices.types.SCALARS) → qcp.matrices.matrix.Matrix[source]¶

Shim layer for the __mul__() operation, so that we can pre-mulitply matrices with a scalar and get the expected behaviour.

Parameters: other (SCALARS) – The scalar to multiply against the matrix
Returns: A new matrix where the elements are scaled by other
Return type: Matrix

__setitem__(i: int, v: qcp.matrices.types.VECTOR)[source]¶

Set the given row in the matrix to the given elements in the list

Parameters

i (int) – The index of the row to modify
v (VECTOR) – The new elements as a list to set the row to.

__str__() → str[source]¶

Create a string representation of the Matrix, with rows separated by newlines, and bounded by ‘[‘/’]’ characters.

Returns: A string representation of the matrix suitable for printing.
Return type: str

__sub__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Subtract the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to subtract from this one.
Returns: A new matrix where the elements are the subtraction of the current and applied matrix elements.
Return type: Matrix

_abc_impl = <_abc._abc_data object>¶

_optional_newline(i: int, N: int) → str[source]¶

Helper function for __str__() to determine which rows require a newline character appended to them.

Parameters

i (int) – The current row index under consideration.
N (int) – The total number of rows.

Returns

A newline character, or empty string depending on the condition.

Return type

str

adjoint() → qcp.matrices.matrix.Matrix[source]¶

Shortcut operation to calculate the transpose and conjugate of the current matrix.

Returns: The new matrix that is transposed and then conjugated of the current matrix.
Return type: MATRIX

columns() → qcp.matrices.types.MATRIX[source]¶

Return the transpose of the matrix as a nested list

Returns: The nested list of matrix elements, indexed by column/row.
Return type: MATRIX

conjugate() → qcp.matrices.matrix.Matrix[source]¶

Calculate the complex conjugate of each matrix element and return a new matrix of these conjugated elements

Returns: The matrix with each element conjugates of the current qcp.matrices.matrix.Matrix
Return type: MATRIX

get_state() → qcp.matrices.types.MATRIX[source]¶

Returns the matrix values as a nested list, indexed by the row/column indices.

Returns: A nested list of the matrix values
Return type: MATRIX

property num_columns: int¶

The number of columns in the Matrix

Returns: The number of columns in the matrix
Return type: int

property num_rows: int¶

The number of rows in the Matrix

Returns: The number of rows in the matrix
Return type: int

property square: bool¶

Whether the matrix is square or not.

Returns: Whether the matrix row/column dimensions match.
Return type: bool

trace() → qcp.matrices.types.SCALARS[source]¶

The sum of the diagonal elements of a square matrix

Returns: The sum of the diagonal of the matrix
Return type: SCALARS

transpose() → qcp.matrices.matrix.Matrix[source]¶

Mirror a square matrix along it’s diagonal, and return a new matrix of these elements

Returns: The transpose of the current matrix.
Return type: MATRIX

property unitary: bool¶

Check if matrix is Unitary (can be shifted to gates.py)

Parameters: Matrix – input: n x n matrix
Returns: Whether the matrix is unitary
Return type: bool

qcp.matrices.sparse_matrix module¶

class qcp.matrices.sparse_matrix.SparseMatrix(state: Union[MATRIX, SPARSE], w: int = - 1, h: int = - 1)[source]¶

Bases: qcp.matrices.matrix.Matrix

Implementation of a Sparse Matrix object, where only the non-zero matrix elements are stored in memory, and if a matrix element is not indexed, it is taken to be zero.

__add__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Add the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to add to this one.
Returns: A new matrix where the elements are the addition of the current and applied matrix elements.
Return type: Matrix

__getitem__(i: int) → qcp.matrices.sparse_matrix.SparseVector[source]¶

Return the row elements for the given row index in a list representation

Parameters: i (int) – The index of the row to get the elements of
Returns: A list containing the row elements
Return type: VECTOR

__init__(state: Union[MATRIX, SPARSE], w: int = - 1, h: int = - 1)[source]¶

Initialise a SparseMatrix, using either a List[List[]] object, or a pre-indexed dictionary mapping indices to non-zero values.

Parameters

state (Union[MATRIX, SPARSE]) – object containing the matrix elements, either by determining the row/column indices from the list, or using the given row/column index mapping.
w (int) – Optional overload of the Matrix width dimension
h (int) – Optional overload of the Matrix height dimension

__len__() → int[source]¶

Return the horizontal size of the SparseMatrix.

Returns: The number of columns in the SparseMatrix
Return type: int

__mul__(other: Union[SCALARS, Matrix]) → Matrix[source]¶

Override of the behaviour of the * multiplication operator.

If the operator is applied using a scalar value to this matrix, the matrix elements are each scaled by this number and a new matrix is returned containing these scaled elements.

If a Matrix object is applied using the * operator, the dot product of the two matrices is calculated, with the current matrix being the first Matrix, and the applied one the second, as order matters for matrix multiplication.

Parameters: other (Union[SCALARS, Matrix]) – The object being applied to this matrix
Returns: A new matrix containing the calculated values as appropriate.
Return type: Matrix

__setitem__(i: int, v: Union[SparseVector, List[SCALARS], Dict[int, SCALARS]])[source]¶

Set the given row in the matrix to the given elements in the list

Parameters

i (int) – The index of the row to modify
v (VECTOR) – The new elements as a list to set the row to.

__str__() → str[source]¶

Create a string representation of the Matrix, with rows separated by newlines, and bounded by ‘[‘/’]’ characters.

Returns: A string representation of the matrix suitable for printing.
Return type: str

__sub__(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Subtract the matching elements of the other matrix to the entries in this matrix, and return a new matrix containing the resultant values.

Parameters: other (Matrix) – The matrix to subtract from this one.
Returns: A new matrix where the elements are the subtraction of the current and applied matrix elements.
Return type: Matrix

_abc_impl = <_abc._abc_data object>¶

_as_list() → qcp.matrices.types.MATRIX[source]¶: Equivalent to get_state()

_dot(other: qcp.matrices.matrix.Matrix) → qcp.matrices.matrix.Matrix[source]¶

Calculate the dot product between this Matrix, and another Matrix.

Parameters: other (Matrix) – The matrix to dot product with this one.
Returns: A new matrix that conforms to the rules of matrix dot producting.
Return type: Matrix

_dot_sparse(other: qcp.matrices.sparse_matrix.SparseMatrix) → qcp.matrices.sparse_matrix.SparseMatrix[source]¶

Optimisation of the _dot() method in the case where both Matrices are SparseMatrix objects, in which case we only need to consider the non-zero entries of the matrices

Parameters: other (SparseMatrix) – The matrix to dot product with this one.
Returns: A new matrix that conforms to the rules of matrix dot producting.
Return type: SparseMatrix

_get_row(i: int) → qcp.matrices.sparse_matrix.SparseVector[source]¶: Equivalent to __getitem__()

columns() → qcp.matrices.types.MATRIX[source]¶

The transpose of the matrix as a nested list

Returns: A nested list of the matrix values transposed, indexed by column/row
Return type: MATRIX

conjugate() → qcp.matrices.sparse_matrix.SparseMatrix[source]¶

Create a new SparseMatrix where each value in the matrix is the complex conjugate of the current matrix values.

Returns: A SparseMatrix object of the same dimensions of the current matrix, with each value conjugated in place.
Return type: SparseMatrix

get_state() → qcp.matrices.types.MATRIX[source]¶

Return the matrix values as a nested list

Returns: A nested list of the matrix values indexed by row/column
Return type: MATRIX

static identity(n: int) → qcp.matrices.sparse_matrix.SparseMatrix[source]¶

Create the identity matrix with the given dimensions

Parameters: n (int) – The matrix dimension
Returns: The SparseMatrix identity matrix object.
Return type: SparseMatrix

property num_columns: int¶

Return the number of columns in the SparseMatrix.

Returns: The number of columns.
Return type: int

property num_rows: int¶

Return the number of rows in the SparseMatrix.

Returns: The number of rows
Return type: int

rows() → qcp.matrices.types.MATRIX[source]¶

Equivalent to get_state().

Returns: A nested list of the matrix values indexed by row/column
Return type: MATRIX

trace() → qcp.matrices.types.SCALARS[source]¶

Calculate the sum of the diagonal elements of the matrix

Returns: The sum of all diagonal elements, with type determined by the value types.
Return type: SCALARS

transpose() → qcp.matrices.sparse_matrix.SparseMatrix[source]¶

Flips the matrix elements along the diagonal, and return a new SparseMatrix containing these values.

Returns: The transpose of the current matrix.
Return type: SparseMatrix

property unitary: bool¶

Check if matrix is Unitary (can be shifted to gates.py)

Parameters: Matrix – input: n x n matrix
Returns: Whether the matrix is unitary
Return type: bool

static zeros(nrow: int, ncol: int = 1) → qcp.matrices.sparse_matrix.SparseMatrix[source]¶

Create a SparseMatrix of given dimensions, where each value of the matrix is zero.

Parameters

nrow (int) – The row dimension of the SparseMatrix
ncol (int) – The (optional) column dimenion of the SparseMatrix defaults to 1, to be a column vector.

Returns

The matrix object of our given size.

Return type

SparseMatrix

class qcp.matrices.sparse_matrix.SparseVector(entries: Union[List[SCALARS], Dict[int, SCALARS]], size: int)[source]¶

Bases: object

Sparse implementation of a row vector, where only the non-zero elements are stored in memory, and any non saved index is taken to be zero.

__getitem__(i: int) → qcp.matrices.types.SCALARS[source]¶

Get the item at the given index in the SparseVector.

Parameters: i (int) – The index of the value to read
Returns: The indexed value.
Return type: SCALARS

__init__(entries: Union[List[SCALARS], Dict[int, SCALARS]], size: int)[source]¶

Create a new SparseVector object, where the values are allocated either directly, by providing a dictionary mapping the indices to the values, or inferred by reading the given list and storing any non-zero list values in a dictionary mapping.

When the dictionary is provided, the vector size is inferred from the highest index in the dictionary, unless the value is overwritten with the size parameter.

Parameters

entries (Union[List[SCALARS], Dict[int, SCALARS]]) – The object containing the vector values to use.
size (int) – The size of the SparseVector

__len__()[source]¶

Return the size of the vector

Returns: The size of the vector
Return type: int

__setitem__(i: int, v: qcp.matrices.types.SCALARS)[source]¶

Set the item at the given index to be the given value.

Parameters

i (int) – The index to modify
v (SCALARS) – The new value to set.

qcp.matrices.sparse_matrix._list_to_dict()[source]¶

Convert a given list of values into a dictionary mapping indices to non-zero values

Parameters

list (vals) – List of vector values.
int (limit) – Optional iteration limit for fixed sized rows.

Returns

dict of key/value pairs for non-zero entries in the list.

Return type

Dict[int, SCALARS]

qcp.matrices.types module¶

qcp.matrices.types.MATRIX¶

Type Alias for the type of the matrix content, a 2D nested list of allowed matrix element types

alias of List[List[Union[complex, float, int]]]

qcp.matrices.types.SCALARS¶

Type Alias for the allowed types for the matrix elements

alias of Union[complex, float, int]

qcp.matrices.types.SCALARS_T = (<class 'complex'>, <class 'float'>, <class 'int'>)¶: Typle Alias for the allowed matrix element types as a tuple

qcp.matrices.types.SPARSE¶

Type Alias for the storage method used in SparseMatrix, the entries of the matrix are stored in a nested dictionary, where values are looked up by row/column index

alias of Dict[int, Dict[int, Union[complex, float, int]]]

qcp.matrices.types.VECTOR¶

Type Alias for the type of a matrix row, as a list representation

alias of List[Union[complex, float, int]]

Module contents¶

Module containing pure Python implementations of matrices.

qcp.matrices.DefaultMatrix¶: Quick type referencing for the preferred Matrix class to use, so that if we want to change it later, all we have to do is modify this line

qcp.matrices package¶

Submodules¶

qcp.matrices.dense_matrix module¶

qcp.matrices.matrix module¶

qcp.matrices.sparse_matrix module¶

qcp.matrices.types module¶

Module contents¶

Quantum Computing Project

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