发表机构
Freie Universität Berlin; Helmholtz-Zentrum Berlin für Materialien und Energie; John A. Paulson School of Engineering and Applied Sciences, Harvard University（柏林自由大学; 亥姆霍兹柏林材料能源中心; 哈佛大学约翰·A·保尔森工程与应用科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出自适应单副本测量算法，以Θ(n)样本复杂度学习任意n量子比特稳定子态，匹配贝尔采样最优性，并扩展至容忍测试及非精确稳定子态。
AI 中文摘要
稳定子态是量子计算的核心，支撑着量子纠错、基准测试和高效经典模拟。然而，其可学习性存在显著差距：一个n量子比特的稳定子态可以通过两次副本的贝尔测量从Θ(n)个副本中学习，而非自适应的单副本测量则需要Ω(n^2)个副本。这里我们表明，适应性完全弥合了这一差距。我们给出一个多项式时间的自适应算法，可以从Θ(n)个单副本Clifford测量中学习任意n量子比特的稳定子态，匹配贝尔采样的最优样本复杂度，而无需任何多副本测量。同样的思想产生一个样本最优的单副本容忍测试器，并且使用k个量子比特的量子内存，在保真度误差ε下，达到最优测试权衡Θ(n-k+1/ε)。最后，我们表明这种自适应机制扩展到精确稳定子态之外：稳定子零度至多为r的态，包括由具有有界数量T门的Clifford电路制备的态，可以使用O(n2^r)个单副本测量来学习。
英文摘要
Stabilizer states are central to quantum computing, underlying quantum error correction, benchmarking, and efficient classical simulation. Yet their learnability exhibits a striking gap: an $n$-qubit stabilizer state can be learned from $Θ(n)$ copies using two-copy Bell measurements, whereas non-adaptive single-copy measurements require $Ω(n^2)$ copies. Here we show that adaptivity completely closes this gap. We give a polynomial-time adaptive algorithm that learns an arbitrary $n$-qubit stabilizer state from $Θ(n)$ single-copy Clifford measurements, matching the optimal sample complexity of Bell sampling without any multi-copy measurements. The same ideas yield a sample-optimal single-copy tolerant tester and, with $k$ qubits of quantum memory, the optimal testing tradeoff $Θ(n-k+1/\varepsilon)$ at infidelity $\varepsilon$. Finally, we show that this adaptive mechanism extends beyond exact stabilizer states: states of stabilizer nullity at most $r$, including states prepared by Clifford circuits with a bounded number of $T$ gates, can be learned using $O(n2^{r})$ single-copy measurements.
Comments17 pages
