Exponential Quantum Space Advantage for Approximating Max-$k$SAT in the Streaming Setting

2026-06-03

AI Summary

In the streaming computation model, classical algorithms for Max-$k$SAT are constrained by space complexity and struggle to surpass an approximation ratio of approximately 0.7071. This work proposes a single-pass quantum streaming algorithm that achieves an approximation ratio of 0.7172 for Max-$k$SAT on $n$ variables using only $\mathrm{polylog}(n)$ space, and further attains a ratio of 0.7425 for Max-2OR. To the best of our knowledge, this is the first demonstration of an exponential quantum space advantage for streaming Max-$k$SAT, and it completes the classification of quantum space advantages across all Boolean Max-2CSP problems.

Abstract

In this paper, we give a one-pass quantum streaming algorithm for Max-$k$SAT that uses $\operatorname{polylog}(n)$ space and achieves a $0.7172$-approximation on instances with $n$ variables. In contrast, prior work by Chou, Golovnev, and Velusamy (FOCS 2020) implies that achieving an approximation ratio better than $\sqrt{2}/2 \approx 0.7071$ for Max-$k$SAT requires $Ω(\sqrt{n})$ space for any classical streaming algorithm. Therefore, it yields an exponential quantum space advantage for Max-$k$SAT in the streaming setting. We further give a one-pass quantum streaming algorithm for Max-2OR that uses $\operatorname{polylog}(n)$ space and achieves a $0.7425$-approximation on instances with $n$ variables. Combining with the known results, it gives a complete classification of quantum space advantages for all Boolean Max-2CSPs.

Problem

• Max-kSAT
• quantum streaming
• space advantage
• approximation ratio
• Boolean Max-2CSPs

Innovation

• quantum streaming algorithm
• exponential space advantage
• Max-kSAT
• approximation ratio
• Max-2CSP