Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size with the number of qubits, more quantum algorithms to find the eigenstates of many-body Hamiltonians will be of wide interest with profound implications and applications. In this work, we advocate a quantum algorithm to find the ground state and excited states of many-body systems, without any penalty functions, variational steps or hybrid quantum-classical steps. Our fully quantum algorithm will be an important addition to the quantum computational toolbox to tackle problems intractable on classical machines.
@article{arxiv.2509.09148,
title = {A penalty-free quantum algorithm to find energy eigenstates},
author = {Nannan Ma and Heng Dai and Jiangbin Gong},
journal= {arXiv preprint arXiv:2509.09148},
year = {2026}
}