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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
In Quantum Sensing, What Beats Beating Noise? Meeting Noise Halfway.
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arXiv · Simon, Sophia, Berry, Dominic W., Somma, Rolando D. · Quantum science preprint
NIST · Quantum science · 2025-09-10
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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.'''<br>
A team including scientists at NIST may have found a new way of dealing with noise at<br>
the microscopic scales where quantum physics reigns.<br>
The article is featured here because it connects current quantum research with a<br>
broader scientific or technological problem.<br>
The preview highlights the main idea while leaving the detailed evidence, figures and<br>
technical discussion to the original source.<br>
Topic area: Quantum science.<br>
Publication or update date: 2025-09-10.<br>
The selected source is NIST; the full article link appears below this preview.<br>
The right-side image is selected from the same article URL when a usable article image<br>
is available.<br>
Readers can follow the source link for the complete article, credits and surrounding<br>
context.
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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.
[https://www.nist.gov/news-events/news/2025/09/quantum-sensing-what-beats-beating-noise-meeting-noise-halfway Read the full article at NIST ->]
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[https://arxiv.org/abs/2605.16195 Read the full article at arXiv ->]
External source: NIST. Selected external quantum article.
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External source: arXiv. Selected external quantum article.
Credits: NIST · 2025-09-10
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Latest revision as of 09:10, 25 May 2026

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Image from or related to the featured external quantum article.

Featured external quantum article

In Quantum Sensing, What Beats Beating Noise? Meeting Noise Halfway.

NIST · Quantum science · 2025-09-10

Article preview.
A team including scientists at NIST may have found a new way of dealing with noise at
the microscopic scales where quantum physics reigns.
The article is featured here because it connects current quantum research with a
broader scientific or technological problem.
The preview highlights the main idea while leaving the detailed evidence, figures and
technical discussion to the original source.
Topic area: Quantum science.
Publication or update date: 2025-09-10.
The selected source is NIST; the full article link appears below this preview.
The right-side image is selected from the same article URL when a usable article image
is available.
Readers can follow the source link for the complete article, credits and surrounding
context.

External source: NIST. Selected external quantum article.

Credits: NIST · 2025-09-10

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