有限量子记忆下的最优稳定子态测试与学习

Quantum Physics

arXiv:2607.02444v1 (quant-ph) [Submitted on 2 Jul 2026]

Title:Optimal Stabilizer Testing and Learning with Limited Quantum Memory

Authors:Srinivasan Arunachalam, Louis Schatzki View a PDF of the paper titled Optimal Stabilizer Testing and Learning with Limited Quantum Memory, by Srinivasan Arunachalam and 1 other authors View PDF HTML (experimental)

Abstract:We study stabilizer state testing and learning with limited coherent quantum memory. Here an algorithm sequentially receives copies of an unknown $n$-qubit state, but may keep only $k$ qubits of coherent quantum memory between measurements. With unrestricted memory, seminal work of Gross, Nezami and Walter showed how to test $n$-qubit stabilizer states using $6$ copies, which is dimension independent, unlike the learning complexity of $\Theta(n)$. We show that this testing-vs-learning separation is lost under memory constraints. More concretely we show that
(1) The sample complexity of testing stabilizer states in the $k$-qubit memory framework is $\Theta(n-k)$. Our upper bound goes via a novel connection to the hidden shift problem and the lower bound is proven using a novel approach to average case bounds on likelihood ratios via combinatorics of the stochastic orthogonal group.
(2) The sample complexity of learning stabilizer states with $k$ qubits of memory, in the non-adaptive framework, is $\Theta(n^2/k)$.
As a further application of our techniques, we prove an exponential lower bound for purity testing even when the memory may be left coherent throughout the protocol. Our main results identify coherent quantum memory as the resource enabling the usual separation between stabilizer testing and learning. In particular, even with $k=0.99n$ qubits of memory, there is no constant-copy stabilizer tester; furthermore for $k=cn$ qubits of memory (for $0< c < 1$), stabilizer testing is as hard as learning, with both requiring $\Theta(n)$ copies.

Comments:	66 pages, 5 figures
Subjects:	Quantum Physics (quant-ph); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Information Theory (cs.IT); Machine Learning (cs.LG)
Cite as:	arXiv:2607.02444 [quant-ph]
	(or arXiv:2607.02444v1 [quant-ph] for this version)
	https://doi.org/10.48550/arXiv.2607.02444 Focus to learn more arXiv-issued DOI via DataCite

Submission history

From: Louis Schatzki [view email]
[v1] Thu, 2 Jul 2026 17:11:38 UTC (2,148 KB)
Full-text links:

Access Paper:

View a PDF of the paper titled Optimal Stabilizer Testing and Learning with Limited Quantum Memory, by Srinivasan Arunachalam and 1 other authors
• View PDF
• HTML (experimental)
• TeX Source

view license

Current browse context:

quant-ph < prev   |   next >
new | recent | 2026-07 Change to browse by: cs
cs.CC
cs.DS
cs.IT
cs.LG
math
math.IT

References & Citations

• INSPIRE HEP
  
• NASA ADS
• Google Scholar
• Semantic Scholar

export BibTeX citation Loading...

BibTeX formatted citation

× Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos

Demos

Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers

Recommenders and Search Tools

Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?)

• Author
• Venue
• Institution
• Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)