Penalty-free quantum algorithm to find energy eigenstates
Phys. Rev. A 113, 042625 – Published 28 April, 2026
DOI: https://doi.org/10.1103/25rr-mpyj
Abstract
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.
