Exponential quantum advantages for decoded quantum interferometry in the streaming setting

Abstract: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.

Quantum Physics (quant-ph); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS)

arXiv:2610.01902 [quant-ph]

(or arXiv:2610.01902v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.01902 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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