Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers

Understand

A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first.

• Today's quantum computers - and even early fault-tolerant quantum computers - are limited in the number of operations they can implement per circuit.
• We introduce quantum algorithms for ground-state energy estimation (GSEE) that accommodate this design constraint.
• The first algorithm estimates ground-state energies, offering a quadratic improvement on the ground state overlap parameter compared to other methods in this regime.