Fix the order of the Lie-Trotter formula in the documentation (#8167)

* Fix the order of the Lie-Trotter formula in the documentation

The Lie-Trotter formula has a second order error [1][2].

[1] https://arxiv.org/pdf/math-ph/0506007.pdf
[2] https://simons.berkeley.edu/sites/default/files/docs/15639/trottererrortheorysimons.pdf

* Second refrence added, where Lie-Trotter scaling is easier to find

Co-authored-by: Luciano Bello <bel@zurich.ibm.com>
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@ -24,7 +24,7 @@ class LieTrotter(ProductFormula):
r"""The Lie-Trotter product formula.
The Lie-Trotter formula approximates the exponential of two non-commuting operators
with products of their exponentials up to a first order error:
with products of their exponentials up to a second order error:
.. math::
@ -35,13 +35,16 @@ class LieTrotter(ProductFormula):
.. math::
e^{-it(XX + ZZ)} = e^{-it XX}e^{-it ZZ} + \mathcal{O}(t).
e^{-it(XX + ZZ)} = e^{-it XX}e^{-it ZZ} + \mathcal{O}(t^2).
References:
[1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders,
"Efficient quantum algorithms for simulating sparse Hamiltonians" (2006).
`arXiv:quant-ph/0508139 <https://arxiv.org/abs/quant-ph/0508139>`_
[2]: N. Hatano and M. Suzuki,
"Finding Exponential Product Formulas of Higher Orders" (2005).
`arXiv:math-ph/0506007 <https://arxiv.org/pdf/math-ph/0506007.pdf>`_
"""
def __init__(