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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Quantum Computing Explained
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arXiv · Simon, Sophia, Berry, Dominic W., Somma, Rolando D. · Quantum science preprint
NIST · Quantum science · 2025-03-18
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'''Article preview.''' We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes an entry of the solution matrix with query complexity $\widetilde{\mathcal{O}}(ν\mathcal{L} t/ε)$, where the constant $ν$ depends on the problem parameters, $\mathcal{L}$ involves a time integral of upper bounds on the norms of evolution operators, and $ε$ is the error. In particular, $ν\mathcal{L}$ is linear in $t$ for unitary dynamics and can be a constant for dissipative dynamics. Our result contrasts prior quantum approaches for differential equations that typically require exponential time for this problem due to the encoding in a quantum state, which can lead to exponentially small amplitudes. We demonstrate the utility of the algorithm through
'''Article preview.''' This emerging technology could change our world.
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The arXiv record is a preprint entry; readers should consult the linked page for the current abstract, subject classification and version history.
The linked source provides the full context, figures and publication details for readers who want to continue beyond this ScholarlyWiki preview.
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[https://arxiv.org/abs/2605.16195 Read the full article at arXiv ->]
[https://www.nist.gov/quantum-information-science/quantum-computing-explained Read the full article at NIST ->]
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External source: arXiv. Selected external quantum article.
External source: NIST. Selected external quantum article.
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Credits: arXiv · Simon, Sophia, Berry, Dominic W., Somma, Rolando D.
Credits: NIST · 2025-03-18
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Revision as of 19:43, 18 May 2026

Image from or related to the featured external quantum article.

Featured external quantum article

Quantum Computing Explained

NIST · Quantum science · 2025-03-18

Article preview. This emerging technology could change our world.

The linked source provides the full context, figures and publication details for readers who want to continue beyond this ScholarlyWiki preview.

External source: NIST. Selected external quantum article.

Credits: NIST · 2025-03-18

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