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Quantum Control and Simulation Using Product Formulas for Exponentials of Commutators

Nathan Wiebe, Institute for Quantum Computing

(Session 6a : Friday from 1:30 - 2:00)

Abstract. This work provides a new recursive method for systematically constructing product formula approximations to exponentials of commutators, giving approximations that are accurate to arbitrarily high order. These formulas are very useful for introducing or suppressing interaction terms in quantum systems, a point that I will illustrate by using our formulas to implement the toric code using only two-body interactions. By presenting an algorithm for quantum search using evolution according to a commutator, I will also show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. I then conclude by showing that our product formulas can be used to improve the scaling of the complexity of certain quantum simulation algorithms with the error tolerance, in the black box setting. This work was done in collaboration with Andrew Childs at the Institute for Quantum Computing.