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Extending Sample-based Quantum Diagonalization to Systems of Linear Equations — arXiv:2610.41708

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41708
License (as archived): CC0-1.0
Archived: 2026-11-02T04:59:33.385Z
SHA-256 of the archived text: c494f250f6ccec6b2815487d36b97dbf4ab0a19fc861adafe2e00dcf5497c5b5
Stable URL of this page: https://metraipolis.com/documento/dc_3d46fffd44cd

How to cite

Extending Sample-based Quantum Diagonalization to Systems of Linear Equations — arXiv:2610.41708 — arXiv (en), https://arxiv.org/abs/2610.41708 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3d46fffd44cd (Metraipolis archive dc_3d46fffd44cd, sha256 c494f250f6ccec6b2815487d36b97dbf4ab0a19fc861adafe2e00dcf5497c5b5)

BibTeX

@misc{dc3d46fffd44cd,
  title = {Extending Sample-based Quantum Diagonalization to Systems of Linear Equations — arXiv:2610.41708},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41708},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3d46fffd44cd; sha256 c494f250f6ccec6b2815487d36b97dbf4ab0a19fc861adafe2e00dcf5497c5b5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41708. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Solving systems of linear equations, $Ax=b$, is a ubiquitous task in computational science. The Harrow-Hassidim-Lloyd algorithm requires phase estimation, controlled rotations, and post-selection, impractical on noisy intermediate-scale quantum hardware. We extend sample-based quantum diagonalization (SQD), developed for quantum chemistry, to linear systems. Following the sample-based Krylov variant, the Hermitian matrix $A$ is decomposed in the Pauli basis, the Trotterized time evolution of $|b\rangle$ is sampled at several times to select computational-basis configurations, and the system is solved classically by a Galerkin projection onto the selected subspace. We prove that the subspace solution is exact when the sampled configurations contain the Krylov support of $b$ and optimal in the energy norm for symmetric positive-definite matrices, so that noise-induced configurations cannot degrade it as long as they do not displace the ideal ones. On IBM Quantum hardware, the sampled distribution of a $4\times4$ example deviates from the exact one by eleven times the shot-noise level, yet the solution is recovered exactly. For a localized problem of dimension $N=1024$, SQD selects 33 configurations, reaches a relative error of $10^{-5}$, and its truncated subspaces coincide with the optimal choice; readout errors enlarge the subspace without degrading the accuracy. The tests also show the limitations: the selected subspace coincides with that of inexpensive classical selection, banded matrices require exponentially many Pauli terms in the binary encoding, and Trotter errors populate spurious configurations unless the circuits are deep. An MIT-licensed Python package and notebooks that reproduce the numerical results are provided.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.41708 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T04:47:42.634Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).