CurrentModule = QuantumLattices.QuantumOperators
Quantum operators form an algebra over a field, which are vector spaces with a bilinear operation (often called the "multiplication") between vectors defined.
With the help of the structure constants of the algebra, the result of the bilinear operation between any arbitrary two vectors can be expressed by a sum of individual ones. Therefore, in principle, an algebra can be represented by the complete basis set of its corresponding vector space and a rank-3 tensor encapsulating its structure constants. It is noted that the "bilinear operation" is not restricted to the usual multiplication. For example, it is the commutator, which is a composition of the usual multiplication and subtraction (for any A and B, the commutator [A, B] is defined as [A, B]≝AB-BA) that serves as the bilinear operator for Lie algebras.
In general, there are three basic operations on quantum operators, i.e. the scalar multiplication between a scalar and a quantum operator, the usual addition and the usual multiplication between quantum operators. Other complicated operations can be composed from these basic ones. These basic operations are implemented in this module.
OperatorUnit is the building block of quantum operators, which specifies the basis of the vector space of the corresponding algebra.
OperatorProd defines the product operator as an entity of basis quantum operators while OperatorSum defines the summation as an entity of OperatorProds. Both of them are subtypes of QuantumOperator, which is the abstract type for all quantum operators.
An OperatorProd must have two predefined contents:
value::Number: the coefficient of the quantum operatorid::ID: the id of the quantum operator
Arithmetic operations (+, -, *, /) between a scalar, an OperatorProd or an OperatorSum is defined. See Manual for details.
Modules = [QuantumOperators]
Order = [:module, :constant, :type, :macro, :function]