IndexedLadderOperator (Encodings)

IndexedLadderOperator Module

Namespace: Encodings
Assembly: Encodings.dll

Fermionic ladder operators with index tracking and ordering predicates.

A LadderOperatorUnit is either Raise j (= a†ⱼ, creation) or Lower j (= aⱼ, annihilation), where j is the spin-orbital index. Products of ladder operators must respect normal ordering (all creation operators to the left of all annihilation operators) and index ordering (within each group, indices are sorted). The functions isInNormalOrder and isInIndexOrder test these conditions. Normal ordering is required before encoding: the Jordan-Wigner and other transforms assume the operator product is in canonical form.

Types

Type	Description
LadderOperatorProductTerm	Represents a product of indexed fermionic ladder operators with a coefficient.
LadderOperatorSumExpression	Represents a sum of ladder operator product terms.
LadderOperatorUnit	Represents the type of a fermionic ladder operator.

Functions and values

Function or value	Description
`isInIndexOrder productTerm` Full Usage: `isInIndexOrder productTerm` Parameters: productTerm : `P<IxOp<uint32, LadderOperatorUnit>>` - The product term to check. Returns: `bool` True if indices are properly ordered; false otherwise.	Checks whether a product term's operators are in index order. Index ordering requires: Raise (creation) operators have ascending indices: a†ᵢ a†ⱼ where i < j Lower (annihilation) operators have descending indices: aₖ aₗ where k > l Combined with normal ordering, this gives the full canonical form. productTerm : `P<IxOp<uint32, LadderOperatorUnit>>` The product term to check. Returns: `bool` True if indices are properly ordered; false otherwise.
`isInNormalOrder productTerm` Full Usage: `isInNormalOrder productTerm` Parameters: productTerm : `P<IxOp<uint32, LadderOperatorUnit>>` - The product term to check. Returns: `bool` True if the term is in normal order; false otherwise.	Checks whether a product term's operators are in normal order. Normal order requires all creation (Raise) operators to appear before all annihilation (Lower) operators: a†ᵢ a†ⱼ ... aₖ aₗ This is the canonical form required by Jordan-Wigner and other encodings. productTerm : `P<IxOp<uint32, LadderOperatorUnit>>` The product term to check. Returns: `bool` True if the term is in normal order; false otherwise.