Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems

TL;DR

This paper introduces a measurement-based quantum simulation method that uses measurements on graph states to efficiently find energy eigenvalues in fermionic systems, potentially reducing runtimes compared to traditional gate-based approaches.

Contribution

It develops a hybrid measurement-based algorithm for fermionic models that leverages graph states and measurement speed advantages for quantum simulation.

Findings

Resource estimates indicate runtime advantages if measurements are faster than gates.

Graph state compactification enhances resource efficiency.

The approach applies to models like Kitaev and Hubbard chains.

Abstract

Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based quantum simulation uses effective time evolution via measurement to allow runtime advantages over conventional circuit-based algorithms that use real-time evolution with quantum gates. We construct a hybrid algorithm to find energy eigenvalues in fermionic models using only measurements on graph states. We apply the algorithm to the Kitaev and Hubbard chains. Resource estimates show a runtime advantage if measurements can be performed faster than gates, and graph states compactification is fully used. In this letter, we set the stage to allow advances in measurement precision to improve quantum simulation.