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