Unified views of quantum simulation algorithms for chemistry

TL;DR

This paper unifies various quantum simulation algorithms for chemistry, clarifying their relationships and advancing towards practical, experimentally feasible algorithms for simulating quantum systems efficiently.

Contribution

It unifies first and second quantized quantum simulation algorithms under a common framework, enabling the development of more practical and efficient methods.

Findings

Unified multiple quantum simulation approaches

Moved towards online second quantized algorithms

Clarified relationships between different measurement algorithms

Abstract

Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical methods. In the past few years, researchers have actively been improving quantum simulation algorithms, especially those in second quantization. This work continues to advance the state-of-the-art by unifying several diverging approaches under a common framework. In particular, it highlights the similarities and differences of the first and second quantized algorithms which are usually presented in a distinct fashion. By combining aspects of the two approaches, this work moves towards an online second quantized algorithm operating within a single-Fock space. This paper also unifies a host of approaches to algorithmic quantum measurement by removing superficial differences. The aim of the effort is not only to give a high-level understanding of quantum simulation, but to move towards experimentally realizable algorithms with practical applications in chemistry and beyond.