Assessing Energy Estimation Algorithms for Early Fault-Tolerant Quantum Computers

Early fault-tolerant quantum computers (FTQCs) are likely to be typified by not only a limited number of logical qubits, but modest logical error rates and the relatively significant overheads associated with implementing non-Clifford operations. Recent years have seen the development of numerous variations on quantum phase estimation (QPE) that promise to be well-adapted to the constraints of early FTQCs – but it is unclear which will achieve the best performance in energy estimation for even the smallest instances. In this contribution, we will compare models of several resource-limited approaches to QPE in terms of robustness to logical errors, the impact of algorithmic errors, and projected runtime as a function of accuracy. We will focus primarily on QPE applied to eigenvalue estimation for Trotterized Hamiltonian simulation, with the aim of staking out resource requirements for small classically simulable benchmark problems that might become viable on systems with thousands of physical qubits.