Fault-tolerant quantum algorithms for quantum molecular systems: A survey

TL;DR

The paper surveys fault-tolerant and early fault-tolerant quantum algorithms for quantum molecular systems, focusing on encoding strategies, advanced Hamiltonian simulation methods, and ground-state energy estimation under EFTQC/FFTQC constraints. It synthesizes core techniques such as block encoding, LCU, and quantum signal processing, and discusses time-dependent and spectral-filter approaches, while addressing potential quantum advantages and dequantization limits. The work highlights practical resource considerations, benchmarks, and a broad landscape of classical alternatives, clarifying where quantum methods may outperform classical counterparts and where the gap remains. It concludes with perspectives on challenges, optimized algorithms, and experimental validation needed to realize EFTQC/FFTQC benefits for quantum chemistry.

Abstract

Solving quantum molecular systems presents a significant challenge for classical computation. The advent of early fault-tolerant quantum computing (EFTQC) devices offers a promising avenue to address these challenges, leveraging advanced quantum algorithms with reduced hardware requirements. This review surveys the latest developments in EFTQC and fully fault-tolerant quantum computing (FFTQC) algorithms for quantum molecular systems, covering encoding schemes, advanced Hamiltonian simulation techniques, and ground-state energy estimation methods. We highlight recent progress in overcoming practical barriers, such as reducing circuit depth and minimizing the use of ancillary qubits. Special attention is given to the potential quantum advantages achievable through these algorithms, as well as the limitations imposed by dequantization and classical simulation techniques. The review concludes with a discussion of future directions, emphasizing the need for optimized algorithms and experimental validation to bridge the gap between theoretical developments and practical implementation in EFTQC and FFTQC for quantum molecular systems.

Figures (1)

• Figure 1: Complexity and performances of various methods in quantum chemistry problems. The accuracies for different methods of solving the electronic structure methods with their computational cost as the system size $n$.