Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints
Abstract
Quantum algorithms that sample basis states and diagonalize a Hamiltonian in their span depend on repairing noisy measurement outcomes, using a constraint native to the target problemunicodex2014typically particle-number symmetry. Many eigenvalue problems possess no such constraint. Here we show that the constraint can instead be engineered into the sampling representation. Using dual-rail encoding, |0⟩→|01⟩ and |1⟩→|10⟩, we implement sampling operations in encoded form, making code-space violations local recovery signals for self-consistent, reference-based repair. On transverse- and mixed-field Ising models of up to 36 spin sites, which lack a U(1) symmetry usable for recovery, code-space recovery reached lower Ritz energies than diagonalization over the full observed support of matched unencoded samples while using 38-84% fewer basis states, despite a twofold qubit overhead. The margin was largest for the two-dimensional and 36-site systems and was already present in the first recovery iteration. Recoverable structure can be engineered rather than inherited.
Related
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BibTeX
@misc{park2026codespace,
title = {{Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints}},
author = {Byeongyong Park and Sanha Kang and Doyeol Ahn and Keunhong Jeong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10227},
eprint = {2607.10227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10227},
}
RIS
TY - UNPB
TI - Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints
AU - Byeongyong Park
AU - Sanha Kang
AU - Doyeol Ahn
AU - Keunhong Jeong
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2607.10227
UR - https://arxiv.org/abs/2607.10227
AB - Quantum algorithms that sample basis states and diagonalize a Hamiltonian in their span depend on repairing noisy measurement outcomes, using a constraint native to the target problemunicodex2014typically particle-number symmetry. Many eigenvalue problems possess no such constraint. Here we show that the constraint can instead be engineered into the sampling representation. Using dual-rail encoding, |0⟩→|01⟩ and |1⟩→|10⟩, we implement sampling operations in encoded form, making code-space violations local recovery signals for self-consistent, reference-based repair. On transverse- and mixed-field Ising models of up to 36 spin sites, which lack a U(1) symmetry usable for recovery, code-space recovery reached lower Ritz energies than diagonalization over the full observed support of matched unencoded samples while using 38-84% fewer basis states, despite a twofold qubit overhead. The margin was largest for the two-dimensional and 36-site systems and was already present in the first recovery iteration. Recoverable structure can be engineered rather than inherited.
ER -