Scholarlink

<p>Quantum computers are believed to bring computational advantages in simulating quantum many-body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems with classical data. Despite examples of learning tasks with provable quantum advantages being proposed, they all involve cryptographic functions and do not represent any physical scenarios encountered in laboratory settings. In this paper, we prove quantum advantages for the physically relevant task of learning quantum observables from classical (measured-out) data. We consider two types of observables: first, we prove a learning advantage for linear combinations of Pauli strings, then we extend our results to a broader case of unitarily parametrized observables. For each case, we delineate sharp boundaries separating physically relevant tasks that admit efficient classical learning from those for which a quantum computer remains necessary for data analysis. Unlike previous works, our classical hardness results rely only on the weaker assumption that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(BQP\)</EquationSource> <EquationSource Format="MATHML"><math> <mstyle mathvariant="sans-serif"> <mi>B</mi> <mi>Q</mi> <mi>P</mi> </mstyle> </math></EquationSource> </InlineEquation> hard processes cannot be simulated by polynomial-size classical circuits, and we also provide a nontrivial quantum learning algorithm. Our results clarify when quantum resources are useful for learning problems in quantum many-body physics, and suggest practical directions in which quantum learning improvements may emerge.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Exponential quantum advantages in learning quantum observables from classical data

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月10日

查看全文
  • Riccardo Molteni,
  • Casper Gyurik,
  • Vedran Dunjko

摘要

Quantum computers are believed to bring computational advantages in simulating quantum many-body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems with classical data. Despite examples of learning tasks with provable quantum advantages being proposed, they all involve cryptographic functions and do not represent any physical scenarios encountered in laboratory settings. In this paper, we prove quantum advantages for the physically relevant task of learning quantum observables from classical (measured-out) data. We consider two types of observables: first, we prove a learning advantage for linear combinations of Pauli strings, then we extend our results to a broader case of unitarily parametrized observables. For each case, we delineate sharp boundaries separating physically relevant tasks that admit efficient classical learning from those for which a quantum computer remains necessary for data analysis. Unlike previous works, our classical hardness results rely only on the weaker assumption that \(BQP\) B Q P hard processes cannot be simulated by polynomial-size classical circuits, and we also provide a nontrivial quantum learning algorithm. Our results clarify when quantum resources are useful for learning problems in quantum many-body physics, and suggest practical directions in which quantum learning improvements may emerge.