SwapOperator

SwapOperator
Produces a unitary operator that swaps two subsystems
Other toolboxes required	none
Related functions	PermutationOperator PermuteSystems Swap SymmetricProjection
Function category	Permutations and symmetry of subsystems

SwapOperator is a function that returns a unitary operator that swaps two subsystems (there may be more than two subsystems overall – the extra subsystems are left alone). The unitary can be chosen to be full or sparse.

Syntax

• S = SwapOperator(DIM)
• S = SwapOperator(DIM,SYS)
• S = SwapOperator(DIM,SYS,SP)

Argument descriptions

• DIM: A specification of the dimensions of the subsystems that S will act on. DIM can be provided in one of two ways:
  • If DIM is a scalar, then all subsystems are assumed to have dimension DIM.
  • If the subsystems have unequal dimensions, DIM should be a vector containing their dimensions.
• SYS (optional, default [1,2]): A 1-by-2 vector containing the indices of the subsystems to be swapped.
• SP (optional, default 0): If set equal to 1, the swap operator is sparse. If equal to 0, the swap operator is full.

Examples

The standard swap operator

The following code produces the operator that swaps two qubits:

>> SwapOperator(2)

ans =

     1     0     0     0
     0     0     1     0
     0     1     0     0
     0     0     0     1

Source code

Click here to view this function's source code on github.