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Quantum-selected configuration interaction: Classical diagonalization of Hamiltonians in subspaces selected by quantum computers

Keita Kanno1,*, Masaya Kohda1,†, Ryosuke Imai1,‡, Sho Koh1, Kosuke Mitarai2,3, Wataru Mizukami2,3, and Yuya O. Nakagawa1

  • 1QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan
  • 2Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
  • 3Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

  • *Contact author: kanno@qunasys.com
  • †Contact author: kohda@qunasys.com
  • ‡Present address: QuEL, Inc., Hachioji ON Building 5F, 4-7-14 Myojincho, Hachioji, Tokyo 192-0046, Japan
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Phys. Rev. Research 8, 023268 – Published 9 June, 2026

DOI: https://doi.org/10.1103/dmn4-snfx

Abstract

We propose quantum-selected configuration interaction, a class of hybrid quantum-classical algorithms for calculating the ground- and excited-state energies of many-electron Hamiltonians on noisy quantum devices. Suppose that an approximate ground state can be prepared on a quantum computer either by variational quantum eigensolver or by some other method. Then, by sampling the state in the computational basis, which is hard for classical computation in general, one can identify the electron configurations that are important for reproducing the ground state. The Hamiltonian in the subspace spanned by those important configurations is diagonalized on classical computers to output the ground-state energy and the corresponding eigenvector. The excited-state energies can be obtained similarly. The result is robust against statistical and physical errors because the noisy quantum devices are used only to define the subspace, and the resulting ground-state energy strictly satisfies the variational principle even in the presence of such errors. The expectation values of various other operators can also be estimated for obtained eigenstates with no additional quantum cost, since the explicit eigenvectors in the subspaces are known. We verified our proposal by numerical simulations and demonstrated it on a quantum device for an eight-qubit molecular Hamiltonian. The proposed algorithms are potentially feasible to tackle some challenging molecules by exploiting quantum devices with several tens of qubits, assisted by high-performance classical computing resources for diagonalization.

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Phys. Rev. Research 8, 023268– Published 9 June, 2026
  • Received 17 March 2023
  • Accepted 9 May 2026
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