Rapid Exponentiation using Discrete Operators: Applications in Optimizing Quantum Controls and Simulating Quantum Dynamics

TL;DR

This paper introduces REDO, a novel method for rapidly approximating matrix exponentiation using discrete operators, significantly accelerating quantum control optimization and quantum dynamics simulations.

Contribution

The paper presents REDO, a new efficient approach for matrix exponentiation that improves computational speed in quantum control and simulation tasks.

Findings

REDO achieves several-fold speed-up in quantum control algorithms.

REDO effectively simulates quantum dynamics with noisy drive fields.

The method is adaptable to systems with time-dependent Hamiltonians.

Abstract

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.