ComplexMPO

Base class: Object

Matrix Product Operator (MPO) of Complex values. Compressed representation of large-dimensional tensors, well suited to the representation of quantum operators for 1D many-body physics problems.

Factories

Heisenberg_1d(integer length, complex transverse_field) -> ComplexMPO

Generate the Hamiltonian Matrix Product Operator (MPO) for the 1D Heisenberg model with Complex values.

Parameters

• length: Number of sites in the chain.
• transverse_field: Strength of the transverse field (default: 0).

Returns

MPO representing the 1D Heisenberg Hamiltonian $H = \sum_i ( S^x_i S^x_{i+1} + S^y_i S^y_{i+1} + S^z_i S^z_{i+1}) + h \sum_i S^x_i$ with open boundary conditions.

Ising_1d(integer length, complex transverse_field) -> ComplexMPO

Generate the Hamiltonian Matrix Product Operator (MPO) for the 1D transverse-field Ising model with Complex values.

Parameters

• length: Number of sites in the chain.
• transverse_field: Strength of the transverse field (default: 0).

Returns

MPO representing the transverse-field Ising Hamiltonian $H = \sum_i S^z_i S^z_{i+1} + h \sum_i S^x_i$ with open boundary conditions.

identity_mpo(integer length, integer physical_size) -> ComplexMPO

Generate an identity Matrix Product Operator (MPO) with Complex values.

Parameters

• length: Number of sites in the MPO chain.
• physical_size: Dimension of the physical (input/output) indices at each site.

Returns

An ComplexMPO representing the identity operator on the full Hilbert space.

identity_mpo(integer length, integer physical_size, as_complex as_complex) -> ComplexMPO

Generate an identity Matrix Product Operator (MPO) with Complex values.

Parameters

• length: Number of sites in the MPO chain.
• physical_size: Dimension of the physical (input/output) indices at each site.
• as_complex:

Returns

An ComplexMPO representing the identity operator on the full Hilbert space.

mpo(const Operator operator) -> ComplexMPO

Convert the supplied Operator to a Matrix Product Operator (MPO) with Complex values.

Parameters

• operator: A symbolic quantum operator. :::warning Not all operation are supported at this time :::

Returns

An ComplexMPO representing the supplied symbolic Operator object.

mpo(const Operator operator, integer size) -> ComplexMPO

Convert the supplied symbolic operator to a Matrix Product Operator (MPO) with Complex values.

Parameters

• operator: A symbolic quantum operator. :::warning Not all operation are support at this time :::
• size: number of sites of the resulting mpo.

Returns

An ComplexMPO representing the suplied symbolic Operator object.

mpo(const Operator operator, as_complex type) -> ComplexMPO

Convert the supplied Operator to a Matrix Product Operator (MPO) with Complex values.

Parameters

• operator: A symbolic quantum operator. :::warning Not all operation are supported at this time :::
• type: The type of the tensor to create.

Returns

An ComplexMPO representing the supplied symbolic Operator object.

mpo(const Operator operator, integer size, as_complex as_complex) -> ComplexMPO

Convert the supplied symbolic operator to a Matrix Product Operator (MPO) with Complex values.

Parameters

• operator: A symbolic quantum operator. :::warning Not all operation are support at this time :::
• size: number of sites of the resulting mpo.
• as_complex:

Returns

An ComplexMPO representing the suplied symbolic Operator object.

random_mpo(integer length, integer physical_size, integer bond_size) -> ComplexMPO

Generate a random Matrix Product Operator (MPO) with Complex values.

Parameters

• length: Number of sites in the MPO chain.
• physical_size: Dimension of the physical (input/output) indices at each site.
• bond_size: Maximum bond dimension between adjacent sites.

Returns

A random ComplexMPO with the specified dimensions. Each site tensor has shape [bond_size, physical_size, physical_size, bond_size].

random_mpo(integer length, integer physical_size, integer bond_size, as_complex as_complex) -> ComplexMPO

Generate a random Matrix Product Operator (MPO) with Complex values.

Parameters

• length: Number of sites in the MPO chain.
• physical_size: Dimension of the physical (input/output) indices at each site.
• bond_size: Maximum bond dimension between adjacent sites.
• as_complex:

Returns

A random ComplexMPO with the specified dimensions. Each site tensor has shape [bond_size, physical_size, physical_size, bond_size].

Constructors

ComplexMPO(integer length) -> ComplexMPO

Matrix Product Operator (MPO) of Complex values with the specified number of sites.

Parameters

• length: Number of sites in the MPO chain.

ComplexMPO(const ComplexMPO other) -> ComplexMPO

Copy constructor for Matrix Product Operator (MPO) of Complex values.

Parameters

• other: The MPO to copy.

Symbols

Name	Description
*	Compute the exact product of a Matrix Product Operator (MPO) with a Matrix Product State (MPS). Applies the quantum operator represented by the MPO to the quantum state represented by the MPS, yielding a new MPS in the same Hilbert space. Both the MPO and MPS must have the same number of sites and physical dimension.
*=	In-place product of two Matrix Product Operators (quantum operators) with Complex values. Composes two quantum operators represented as Matrix Product Operators.
+	Compute the sum of two Matrix Product Operators (quantum operators) with Complex values.
+=	In-place addition of two Matrix Product Operators (MPO) with Complex values.
-	Compute the difference of two Matrix Product Operators (MPO) with Complex values.
-=	In-place subtraction of two Matrix Product Operators (MPO) with Complex values.
/	Scalar division of an Matrix Product Operator (MPO) with Complex values.
/=	In-place scalar division of an Matrix Product Operator (MPO) with Complex values.
=	Assignment operator for Matrix Product Operator (MPO) of Complex values.
[]	Access a specific site tensor in the Matrix Product Operator (MPO) chain by index. Supports negative indexing (e.g., -1 for the last site).

Members

Name	Description
capacity	Get the current capacity of the Matrix Product Operator (MPO).
expval	Compute the expectation value $\langle \psi \| \hat{O} \| \psi \rangle$ of a quantum operator in state $\|\psi\rangle$ in a Matrix Product State (MPS) encoded state.
get_site	Get a copy of the site tensor in the Matrix Product Operator (MPO) at the specified index.
matrix	Convert an Matrix Product Operator (MPO) to a full matrix representation.
max_bond	Get the maximum bond dimension across all bonds in the MPO chain.
open_boundary	Set the Matrix Product Operator (MPO) to open boundary conditions.
periodic_boundary	Set the Matrix Product Operator (MPO) to periodic (closed) boundary conditions.
push_back	Append a site tensor to the end of the Matrix Product Operator (MPO).
reserve	Reserve capacity for the Matrix Product Operator (MPO). Used as system size for otherwise uninitialized mpo operation with Operators
resize	Resize a Matrix Product Operator (MPO) to a target size with empty tensors for position beyond the current end of the MPO.
set_boundary_like	Copy the boundary conditions from another Matrix Product Operator (MPO) or Matrix Product State (MPS).
set_site	Set the site tensor at the specified index in the Matrix Product Operator (MPO).
size	Get the number of sites in the MPO.