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arXiv · 2509.09148

A penalty-free quantum algorithm to find energy eigenstates

Nannan Ma·Heng Dai·Jiangbin Gong
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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.

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Nannan Ma, Heng Dai, Jiangbin Gong. 2025-09-11. A penalty-free quantum algorithm to find energy eigenstates. https://doi.org/10.1103/25rr-mpyj

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