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arXiv 2403.03469quant-ph
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利用共轭态和最小量子存储器实现指数级学习优势

Exponential learning advantages with conjugate states and minimal quantum memory

Robbie King, Kianna Wan, Jarrod McClean

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AI总结：

本文提出利用未知态及其复共轭 $ρ\otimes ρ^\ast$ 作为量子学习资源，证明在最小量子存储器下影子层析可获得指数优势，并刻画其物理应用。

摘要：

量子计算机能够直接操控和分析存储在量子存储器中的量子态，这使其能够了解物理世界中在测量次数有限时原本不可见的方面。本文研究一种未来量子计算机可能获得的新型学习资源——对未知态及其复共轭 $ρ\otimes ρ^\ast$ 一并进行测量。对于某一影子层析任务，我们意外发现，即使 K 很大，仅测量 $ρ\otimes ρ^\ast$ 的副本也能比测量 $ρ^{\otimes K}$ 强指数倍。这扩展了仅使用常数开销量子存储器（即最小量子存储器）即可证明具有指数优势的任务类别，并且我们给出了若干在计算和物理应用中自然存在 $ρ^\ast$ 的例子。此外，我们在广义 Clifford 系综下精确量化了单副本上经典影子的能力，并给出一类可被高效学习的量。我们在单副本和量子存储器两种设定下研究的学习任务都具有自然的物理意义，对应于玻色模式取极限时的实空间可观测量，并在噪声背景下检测特定信号时实现指数级提升。我们量化了量子学习中一种强大的新资源，并相信该优势可能应用于改进量子模拟、从量子传感器中学习以及揭示新的物理现象。

英文摘要：

The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements. Here we investigate a new learning resource which could be available to quantum computers in the future -- measurements on the unknown state accompanied by its complex conjugate $ρ\otimes ρ^\ast$. For a certain shadow tomography task, we surprisingly find that measurements on only copies of $ρ\otimes ρ^\ast$ can be exponentially more powerful than measurements on $ρ^{\otimes K}$, even for large $K$. This expands the class of provable exponential advantages using only a constant overhead quantum memory, or minimal quantum memory, and we provide a number of examples where the state $ρ^\ast$ is naturally available in both computational and physical applications. In addition, we precisely quantify the power of classical shadows on single copies under a generalized Clifford ensemble and give a class of quantities that can be efficiently learned. The learning task we study in both the single copy and quantum memory settings is physically natural and corresponds to real-space observables with a limit of bosonic modes, where it achieves an exponential improvement in detecting certain signals under a noisy background. We quantify a new and powerful resource in quantum learning, and we believe the advantage may find applications in improving quantum simulation, learning from quantum sensors, and uncovering new physical phenomena.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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