发表机构
California Institute of Technology; University of Southern California（加州理工学院; 南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文在流式设置下证明解码量子干涉测量（DQI）算法在内存方面具有可证明的指数级量子优势，通过改编算法满足93%的约束，而任何经典算法满足76%的约束都需要多项式空间。
AI 中文摘要
解码量子干涉测量（DQI）是由Jordan等人（Nature 2025）提出的多项式时间量子算法。对于已知为最优多项式交集（OPI）的自然优化问题，该算法在已知所有经典算法都需要指数时间的机制中实现了近似保证。除了时间，空间是另一个核心资源：存储和处理大规模输入可能非常具有挑战性，特别是当逻辑量子比特承担大量容错实现开销时。这激发了以下问题：DQI是否在内存方面产生量子优势，我们能否无条件证明这一点？我们在流式设置中对此问题给出了肯定回答。特别地，我们考虑使用Hermite插值和Hasse导数的OPI的自然推广，该问题要求一个低次多项式尽可能多地满足其值和导数上的约束。作为一个具体例子，我们展示[量子效率] DQI算法的一种改编产生满足93%约束的多项式；此外，它仅单次读取输入流，使用多对数空间，并且每个流条目的计算时间为多对数。[经典难度] 任何产生仅满足76%约束的答案的经典算法都需要多项式空间，即使它可以读取输入流多项式多次并且可以使用无限时间。我们的结果提供了可调参数的完整权衡曲线，并暗示DQI对于原始OPI问题具有可证明的量子优势。
英文摘要
Decoded quantum interferometry (DQI) is a polynomial-time quantum algorithm introduced by Jordan et al. (Nature 2025). For a natural optimization problem, known as optimal polynomial intersection (OPI), it achieves approximation guarantees in regimes where all known classical algorithms require exponential time. Besides time, space is another central resource: storing and manipulating a massive input can be very challenging, especially when logical qubits carry substantial fault-tolerant implementation overhead. This motivates the following question: does DQI yield quantum advantages in memory, and can we prove it unconditionally? We give an affirmative answer to this question in the streaming setting. In particular, we consider a natural generalization of OPI using Hermite interpolation and Hasse derivatives, which asks for a low-degree polynomial satisfying as many constraints on its values and derivatives as possible. As a concrete example, we show [Quantum efficiency.] An adaptation of the DQI algorithm produces a polynomial satisfying $93\%$ of the constraints; moreover, it only reads the input stream in one pass, uses polylogarithmic space, and has polylogarithmic computation time per stream entry. [Classical hardness.] Any classical algorithm that produces an answer satisfying just $76\%$ of the constraints requires polynomial space, even if it can read the input stream with polynomially many passes and can use unlimited time. Our result provides a complete tradeoff curve for the tunable parameters, and implies that DQI has provable quantum advantages for the original OPI problem.
