Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention, the numerical evaluation of ME remains computationally expensive, particularly for large dimensions. Often this process becomes a bottleneck in algorithms requiring iterative evaluation of ME. Here we propose a method for approximating ME of a single operator with a bounded coefficient into a product of certain discrete operators. This approach, which we refer to as Rapid Exponentiation using Discrete Operators (REDO), is particularly efficient for iterating ME over large numbers. We describe REDO in the context of a quantum system with a constant as well as a time-dependent Hamiltonian, although in principle, it can be adapted in a more general setting. As concrete examples, we choose two applications. First, we incorporate REDO in optimal quantum control algorithms and report a speed-up of several folds over a wide range of system size. Secondly, we propose REDO for numerical simulations of quantum dynamics. In particular, we study exotic quantum freezing with noisy drive fields.
Optimizing two-qubit gates for ultracold fermions in optical lattices
Forschungszentrum Jülich GmbH（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）
