MPS combination (MPSSum)

Matrix-product states can be operated as normal quantum states, adding, rescaling or subtracting them, as you would normally do with vectors. However, when doing so, SeeMPS never really transform the states. Instead, it keeps track of the operations in a MPSSum structure.

For instance, you could combine two MPS states as follows

>>> mps1 = random_uniform_mps(2, 10)
>>> mps2 = product_state([1.0, 0.0], 10)
>>> mps3 = 0.5 * mps1 - 0.3 * mps2
>>> print(mps3)
<seemps.state.mps.MPSSum object at 0x00000117FACDF490>

The result in mps3 is a temporary object with the weights

>>> mps3.weights
[1, -1]

and mps3.states[0] and mps3.states[1] contain rescaled versions of mps1 and mps2.

In addition to creating the sums implicitly, you can also create them explicitly using the classes’ constructor.

MPSSum(weights, states[, check_args])

Class representing a weighted sum (or difference) of two or more MPS.

Conversions

An MPSSum can be approximated by a matrix-product state through an algorithm known as “simplification”, explained in the algorithms section. It can also be converted to an MPS (with possibly quite large bond dimensions) and to standard wavefunctions.

join()	Create an MPS by combining all tensors from all states in the linear combination.
to_vector()	Return the wavefunction of this quantum state.