Tensor Product¶
Abstract tensor product.

class
sympy.physics.quantum.tensorproduct.
TensorProduct
[source]¶ The tensor product of two or more arguments.
For matrices, this uses
matrix_tensor_product
to compute the Kronecker or tensor product matrix. For other objects a symbolicTensorProduct
instance is returned. The tensor product is a noncommutative multiplication that is used primarily with operators and states in quantum mechanics.Currently, the tensor product distinguishes between commutative and non commutative arguments. Commutative arguments are assumed to be scalars and are pulled out in front of the
TensorProduct
. Noncommutative arguments remain in the resultingTensorProduct
.Parameters: args : tuple
A sequence of the objects to take the tensor product of.
Examples
Start with a simple tensor product of sympy matrices:
>>> from sympy import I, Matrix, symbols >>> from sympy.physics.quantum import TensorProduct >>> m1 = Matrix([[1,2],[3,4]]) >>> m2 = Matrix([[1,0],[0,1]]) >>> TensorProduct(m1, m2) Matrix([ [1, 0, 2, 0], [0, 1, 0, 2], [3, 0, 4, 0], [0, 3, 0, 4]]) >>> TensorProduct(m2, m1) Matrix([ [1, 2, 0, 0], [3, 4, 0, 0], [0, 0, 1, 2], [0, 0, 3, 4]])
We can also construct tensor products of noncommutative symbols:
>>> from sympy import Symbol >>> A = Symbol('A',commutative=False) >>> B = Symbol('B',commutative=False) >>> tp = TensorProduct(A, B) >>> tp AxB
We can take the dagger of a tensor product (note the order does NOT reverse like the dagger of a normal product):
>>> from sympy.physics.quantum import Dagger >>> Dagger(tp) Dagger(A)xDagger(B)
Expand can be used to distribute a tensor product across addition:
>>> C = Symbol('C',commutative=False) >>> tp = TensorProduct(A+B,C) >>> tp (A + B)xC >>> tp.expand(tensorproduct=True) AxC + BxC

sympy.physics.quantum.tensorproduct.
tensor_product_simp
(e, **hints)[source]¶ Try to simplify and combine TensorProducts.
In general this will try to pull expressions inside of
TensorProducts
. It currently only works for relatively simple cases where the products have only scalars, rawTensorProducts
, notAdd
,Pow
,Commutators
ofTensorProducts
. It is best to see what it does by showing examples.Examples
>>> from sympy.physics.quantum import tensor_product_simp >>> from sympy.physics.quantum import TensorProduct >>> from sympy import Symbol >>> A = Symbol('A',commutative=False) >>> B = Symbol('B',commutative=False) >>> C = Symbol('C',commutative=False) >>> D = Symbol('D',commutative=False)
First see what happens to products of tensor products:
>>> e = TensorProduct(A,B)*TensorProduct(C,D) >>> e AxB*CxD >>> tensor_product_simp(e) (A*C)x(B*D)
This is the core logic of this function, and it works inside, powers, sums, commutators and anticommutators as well:
>>> tensor_product_simp(e**2) (A*C)x(B*D)**2