发表机构
CQST, IIIT Hyderabad; CSTAR, IIIT Hyderabad; QSL, University of Edinburgh（海德拉巴信息技术研究所量子科学中心; 海德拉巴信息技术研究所计算科学与技术研究; 爱丁堡大学量子系统实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明量子系统中催化剂能极大提升计算功提取效率，实现全部遍历功提取，而非催化过程提取可忽略，并引入伪遍历功概念，揭示催化计算与遍历功的深层联系。
AI 中文摘要
我们证明了最大分离：$n$ 量子比特系统可以具有 $\Theta(n)$ 的遍历功（ergotropy），而每个高效过程提取的功可忽略不计，即使对于由单量子比特项组成的哈密顿量也是如此。我们建立了无条件的存在性分离，并在随机预言机模型中给出了显式构造。假设存在量子安全伪随机函数，这种分离可以扩展到普通模型。这项工作揭示了遍历功与催化计算复杂性之间的重要联系——催化计算是指辅助量子比特最终必须恢复到其初始状态的计算。相对于随机预言机，我们建立了关系和决策问题，这些问题是：（i）可以用 $\lambda$ 个催化剂高效解决；但（ii）对于任何 $c<1$，任何算法都不能用 $c\lambda$ 个催化剂解决。我们通过证明量子空间受限算法的查询下界来证明这一点。因此，对于计算遍历功，催化剂被证明是令人惊讶地强大——存在一族哈密顿量和态，对于这些哈密顿量和态，催化剂能够高效提取全部 $\Theta(n)$ 遍历功，而每个高效的非催化过程提取的功可忽略不计。此外，催化剂还允许我们引入并实例化伪遍历功（pseudoergotropy）的概念——类似于伪随机性。另一方面，我们表明催化剂不会改变（信息论上的）遍历功。最后，我们的工作也揭示了问题的经典方面。首先，我们的大多数构造依赖于经典态和哈密顿量，因此也暗示了经典遍历功的类似结果。其次，我们表明某些量子性证明协议可用于一般性地区分经典和量子催化遍历功。
英文摘要
We prove maximal separations: $n$-qubit systems can have $Θ(n)$ ergotropy, while every efficient process extracts negligible work, even for Hamiltonians consisting of single-qubit terms. We establish an unconditional existential separation and give an explicit construction in the random oracle model. Assuming the existence of quantum-secure pseudorandom functions, this separation extends to the plain model. This work uncovers an important connection between ergotropy and the complexity of catalytic computation---computation where auxiliary qubits must be finally restored to their initial state. Relative to a random oracle, we establish relational and decision problems that: (i) can be solved efficiently with $λ$ catalysts; but (ii) cannot be solved by any algorithm with $cλ$ catalysts, for any $c<1$. We show this by proving query lower bounds for quantum-space bounded algorithms. As a consequence, for computational ergotropy, catalysts prove to be surprisingly powerful---there is a family of Hamiltonians and states for which catalysts enable efficient extraction of the full $Θ(n)$ ergotropy, while every efficient non-catalytic process extracts negligible work. Furthermore, catalysts also allow us to introduce and instantiate the notion of pseudoergotropy---analogous to pseudorandomness. On the other hand, we show catalysts do not change (information-theoretic) ergotropy. Finally, our work also sheds light on the classical aspect of the problem. First, most of our constructions rely on classical states and Hamiltonians and therefore imply analogous results for classical ergotropy. Second, we show that certain proof of quantumness protocols can be used to generically separate classical and quantum catalytic ergotropy.
Comments70 pages, 3 Figures; See https://atulsingharora.github.io/cat for updates
