Finding Exponential Product Formulas of Higher Orders

By Naomichi Hatano, Masuo Suzuki. 2005

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This article is based on a talk presented at a conference “Quantum Annealing and Other Optimization Methods” held at Kolkata, India on March 2–5, 2005. It will be published in the proceedings “Quantum Annealing and Other Optimization Methods” (Springer, Heidelberg) pp. 39–70. In the present article, we review the progress in the last two decades of the work on the Suzuki-Trotter decomposition, or the exponential product formula. The simplest Suzuki-Trotter decomposition, or the well-known Trotter decomposition [1–4] is given by e x(A+B) = e xA e xB + O(x 2 ), (1) where x is a parameter and A and B are arbitrary operators with some commutation relation [A, B] 6 0. Here the product of the exponential operators on the right-hand side is regarded as an approximate decomposition of the exponential operator on the left-hand side with correction terms of the second order of x. Mathematicians put Eq. (1) in the form e xA e xB = e x(A+B)+O(x 2 ) (2)

Subfields: Artificial Intelligence, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ffeae87c0fd696d5439c70f30bfe44b5ced43b83

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Citations in the corpus

Simulating chemistry using quantum computers. (2010, background): “The approximation can be improved by increasing the number of time steps or by using higher-order generalizations of this formula (54,18).”
An adaptive variational algorithm for exact molecular simulations on a quantum computer (2018, methodology): “This is achieved by using a Trotter expansion of a matrix exponential [34],”