Towards Hamiltonian Simulation with Decision Diagrams

TL;DR

This paper introduces a new Hamiltonian simulation method using Decision Diagrams, which can outperform existing techniques in certain cases by exploiting redundancies in quantum state representations.

Contribution

It presents the first application of Decision Diagrams to Hamiltonian simulation, demonstrating their potential advantages and limitations through evaluation.

Findings

DDs can provide orders of magnitude improvement in some cases

The approach offers a promising alternative for complex quantum systems

Limitations of DDs are also identified and discussed

Abstract

This paper proposes a novel approach to Hamiltonian simulation using Decision Diagrams (DDs), which are an exact representation based on exploiting redundancies in representations of quantum states and operations. While the simulation of Hamiltonians has been studied extensively, scaling these simulations to larger or more complex systems is often challenging and may require approximations or new simulation methods altogether. DDs offer such an alternative that has not yet been applied to Hamiltonian simulation. In this work, we investigate the behavior of DDs for this task. To this end, we review the basics of DDs such as their construction and present how the relevant operations for Hamiltonian simulation are implemented in this data structure -- leading to the first DD-based Hamiltonian simulation approach. Based on several series of evaluations and comparisons, we then discuss insights about the performance of this complementary approach. Overall, these studies show that DDs indeed may offer a promising new data structure which, for certain examples, can provide orders of magnitudes of improvement compared to the state-of-the-art, yet also comes with its own, fundamentally different, limitations.