Operator

Base class for all quantum operators.

Factories

`operator_free(const ComplexSparseMatrix matrix) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Unless specified otherwise, using the factory operator_free on an operator will default to complex. Valid options include (as_real, as_complex, unspecified) | (as_fermion, unspecified) | (as_singleparticle, unspecified) | (as_sparse, unspecified) and will default to (as_complex | as_fermion | as_singleparticle | as_sparse) respectively. When used on a matrix, the scalar field defaults to that of the provided matrix unless specified otherwise.

Parameters

matrix: The matrix representation of the free operator.

`operator_free(const RealMatrix matrix) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the free operator.

`operator_free(const Operator operator) -> Operator`

Generates an operator that represents the hopping terms of the input operator.

Parameters

operator: The operator representing a sum of hopping terms.

`operator_free(const ComplexMatrix matrix) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the free operator.

`operator_free(const RealSparseMatrix matrix) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the free operator.

`operator_free(const RealSparseMatrix matrix, as_complex options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexSparseMatrix matrix, as_complex options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const Operator operator_sum, as_complex options) -> Operator`

Generates an operator that represents the hopping terms of the input operator.

Parameters

operator_sum: The operator sum.
options: A set of options used to dispatch the appropriate operator.

`operator_free(const Operator operator_sum, as_real options) -> Operator`

Generates an operator that represents the hopping terms of the input operator.

Parameters

operator_sum: The operator sum.
options: A set of options used to dispatch the appropriate operator.

`operator_free(const Operator operator_sum, const StateInfo options) -> Operator`

Generates an operator that represents the hopping terms of the input operator.

Parameters

operator_sum: The operator sum.
options: A set of options used to dispatch the appropriate operator.

`operator_free(const RealSparseMatrix matrix, const StateInfo options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const RealMatrix matrix, as_real options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const RealMatrix matrix, as_complex options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const RealMatrix matrix, const StateInfo options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexSparseMatrix matrix, as_real options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexMatrix matrix, as_complex options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexMatrix matrix, as_real options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexMatrix matrix, const StateInfo options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const ComplexSparseMatrix matrix, const StateInfo options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_free(const RealSparseMatrix matrix, as_real options) -> Operator`

Generates an operator that represents the hopping terms of the input matrix.

Parameters

matrix: The matrix representation of the single-particle operator.
options: A set of options used to specify the single particle operator type.

`operator_stencil(const Map options) -> Operator`

Generates a stencil operator.

A free stencil represents an operator of the form $\sum_{s}\sum_{n=0}^N \alpha_{n}c_{s}^{\dagger}c_{s + \delta_n}$ where $\delta_n$ are displacement vectors, $s$ are lattice position vectors, the $\alpha_n$ are position independent coefficients and $N$ is the number of such coefficients.To construct a stencil, the above parameters must be passed explicitly, together with information about the lattice dimensions and the boundary conditions.

Parameters

options: An option map to specify the parameters of the stencil.

Example

var stencil_vectors = [[-1,0],[1,0],[0,1],[0,-1]] //[[delta_{0,x},delta_{0,y}],[delta_{1,x},delta_{1,y}],[delta_{2,x},delta_{2,y}],[delta_{3,x},delta_{3,y}]]
var dimensions = [50,40] // [L_x, L_y]
var stencil_values = [0.5 + 1i, 0.2 + 1i, 0.3 + 0.1i, 2i + 2] // [alpha_0, alpha_1, alpha_2, alpha_3]
var boundary_conditions = [boundary_condition.periodic, boundary_condition.open]
var stencil = operator_stencil(["displacements":stencil_vectors,"dimensions":dimensions,"values":stencil_values,"boundary_conditions":boundary_conditions])

`operator_stencil(const List<List<integer>> displacement_vectors", "The displacement vectors $\delta_n$ of the stencil., const List<integer> dimensions, const List<real> stencil_values", "The stencil values $\alpha_n$, const List<BC> boundary_conditions) -> Operator`

Generates a stencil operator.

Parameters

displacement_vectors", "The displacement vectors $\delta_n$ of the stencil.:
dimensions: The dimensions of the underlying lattice.
stencil_values", "The stencil values $\alpha_n$ :
boundary_conditions: The boundary conditions of the lattice.

Example

var stencil_vectors = [[-1,0],[1,0],[0,1],[0,-1]] //[[delta_{0,x},delta_{0,y}],[delta_{1,x},delta_{1,y}],[delta_{2,x},delta_{2,y}],[delta_{3,x},delta_{3,y}]]
var dimensions = [50,40] // [L_x, L_y]
var stencil_values = [0.5 + 1i, 0.2 + 1i, 0.3 + 0.1i, 2i + 2] // [alpha_0, alpha_1, alpha_2, alpha_3]
var boundary_conditions = [boundary_condition.periodic, boundary_condition.open]
var stencil = operator_stencil(["displacements":stencil_vectors,"dimensions":dimensions,"values":stencil_values,"boundary_conditions":boundary_conditions])

`operator_stencil(const List<List<integer>> displacement_vectors", "The displacement vectors $\delta_n$ of the stencil., const List<integer> dimensions, const List<complex> stencil_values", "The stencil values $\alpha_n$, const List<BC> boundary_conditions) -> Operator`

Generates a stencil operator.

Parameters

displacement_vectors", "The displacement vectors $\delta_n$ of the stencil.:
dimensions: The dimensions of the underlying lattice.
stencil_values", "The stencil values $\alpha_n$ :
boundary_conditions: The boundary conditions of the lattice.

Example

var stencil_vectors = [[-1,0],[1,0],[0,1],[0,-1]] //[[delta_{0,x},delta_{0,y}],[delta_{1,x},delta_{1,y}],[delta_{2,x},delta_{2,y}],[delta_{3,x},delta_{3,y}]]
var dimensions = [50,40] // [L_x, L_y]
var stencil_values = [0.5 + 1i, 0.2 + 1i, 0.3 + 0.1i, 2i + 2] // [alpha_0, alpha_1, alpha_2, alpha_3]
var boundary_conditions = [boundary_condition.periodic, boundary_condition.open]
var stencil = operator_stencil(["displacements":stencil_vectors,"dimensions":dimensions,"values":stencil_values,"boundary_conditions":boundary_conditions])

Symbols

Name	Description
`!=`	Compares two Operator objects for inequality. Returns true if the operators differ in type or internal structure.
`*`	Multiplies two operators together, creating a product operator.
`+`	Adds two operators together. Returns a generic Operator for basic additions, ComplexOperatorSum when explicitly working with complex coefficients.
`-`	Subtracts one operator from another. Returns a generic Operator for basic subtractions, ComplexOperatorSum when explicitly working with complex coefficients.
`==`	Compares two operators for equality.Two operators are equal if they are the same type and have identical parameters.Note that mathematically equivalent expressions may not be considered equal
`>>`	In-place Operator-vector product operator.

Members

Name	Description
expval	Computes the expectation value of an Operator for a given state. Calculates < $\psi$ \|O\| $\psi$ >, where $\psi$ is a quantum state and $O$ is an operator.
name	Returns the name of an individual operator as a string. Note: This function only works with individual operators (X, Y, Z, XX, YY, etc.), not for OperatorProduct or OperatorSum.
norm	Computes the spectral norm (largest singular value) of the operator. Can be called using either function call syntax norm(op) or method call syntax op.norm().
sites	Returns the sites of an individual operator in definition order. Unlike support(), this preserves the order of sites as they appear in the operator definition. Note: This function only works with individual operators (X, Y, Z, XX, YY, etc.). For OperatorProduct or OperatorSum, use support() instead. Important: The order returned is the constructor order, not necessarily the order of mathematical application.
support	Returns the support of the operator (the set of qubits it acts on) .Current limitation: This version only supports OperatorProduct and single operators. OperatorSum support may not work correctly in this version.

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