MPO¶

Matrix product operator.

MPO ¶

MPO(
    tensors: List[Tensor],
    bc: str = "OBC",
    center: Optional[int] = None,
    itag_prefix: Optional[str] = None,
)

Bases: Network

Matrix product operator.

Each site tensor has axes (left_bond, right_bond, phys_in, phys_out) where:

phys_in (ket, axis 2) and phys_out (bra, axis 3) both carry itag s{i:02d} at site i, differentiated by opposite directions.
Contracting an MPS ket (s{i:02d}, IN) against this MPO is automatic: the MPO bra (s{i:02d}, OUT) pairs with the MPS ket.

Parameters:

Name	Type	Description	Default
`tensors`	`List[Tensor]`	List of site tensors, each with exactly 4 axes `(left_bond, right_bond, phys_in, phys_out)`. Both physical axes at site i must carry itag `s{i:02d}` with opposite directions.	required
`bc`	`str`	Boundary condition: `'OBC'` (default) or `'PBC'`.	`'OBC'`
`center`	`Optional[int]`	Orthogonality center site index, or `None` if unspecified.	`None`
`itag_prefix`	`Optional[str]`	Bond itag prefix string. Defaults to `'W'` when `None`.	`None`

Raises:

Type	Description
`ValueError`	If any tensor has the wrong axis count, incorrect physical itags, physical axes with the same direction, or adjacent bond indices are inconsistent.

Functions¶

compact ¶

compact(trunc: Optional[dict] = None) -> None

Compress the MPO bond dimensions in-place with norm preservation.

Performs a two-sweep canonicalization:

Left-to-right sweep without truncation, moving the orthogonality center to the rightmost site. This concentrates the full operator norm into the center tensor.
Normalize the center tensor to unit Frobenius norm, temporarily factoring out the overall scale.
Right-to-left sweep with SVD truncation (controlled by trunc), moving the center to site 0. Because the environment is unit-normed, the truncation threshold is applied on a consistent scale.
Restore the overall scale into the new center tensor, then call redistribute_norm() to spread it evenly across all sites.

Parameters:

Name	Type	Description	Default
`trunc`	`Optional[dict]`	Truncation options forwarded to `canonical()` during the right-to-left compression sweep. Defaults to `{'thresh': 1e-14}` when `None`.	`None`

redistribute_norm ¶

redistribute_norm() -> None

Redistribute the MPO norm equally across all site tensors.

Computes the total Frobenius norm N, multiplies every site tensor by factor = N^(1/L), then divides the center tensor by N to remove the excess. The product of all scale factors is factor^L / N = 1, so the operator and its total norm are preserved. center is reset to None because the per-site rescaling breaks any prior canonical form.

Raises:

Type	Description
`ValueError`	If `center` is `None` (the MPO must be in canonical form so the norm is concentrated in a well-defined center tensor).
`ValueError`	If the MPO norm is numerically zero (e.g. due to norm decay).

String Representation¶

repr(mpo) (and therefore the interactive display in notebooks and REPLs) renders a text diagram of the chain:

               Matrix Product Operator (MPO)                
               ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾                
           ╷   ╷   ╷   ╷     ╷     ╷   ╷   ╷   ╷            
           □───□───□───□─···─⊡─···─□───□───□───□            
           ╵   ╵   ╵   ╵     ╵     ╵   ╵   ╵   ╵            
               length: 100     max bond: 64
               center: 49      norm: 1.00e+00

Chain row — each node is one site; consecutive sites are joined by ───. When the chain is too long to show in full, a gap ─···─ is inserted and only a subset of sites near the edges and center is displayed.

Physical-index rows — the downward stub ╵ beneath each node is the physical-input (ket) index; the upward stub ╷ above is the physical-output (bra) index.

Node symbols:

Symbol	Meaning
`□`	Regular site
`⊡`	Orthogonality center (`center` attribute)

Info block — length is the number of sites L; max bond is the largest bond dimension across all virtual indices; center is the orthogonality center index (None if not set); norm is ‖O‖.