Dequantizing Short-Path Quantum Algorithms

2026-04-13

AI Summary

This work investigates whether short-path quantum algorithms can achieve super-quadratic quantum speedups for constraint satisfaction problems (MAX-k-CSP). By uncovering an inherent classical simulability mechanism, the authors explicitly reconstruct and dequantize the core component of the quantum algorithm for the first time. Leveraging this insight, they devise a classical algorithm with runtime \(2^{(1-c')n}\), where \(c' > c\), which outperforms the original quantum algorithm’s complexity of \(2^{(1-c)n/2}\). This result refutes the claimed super-quadratic quantum advantage and establishes a novel paradigm for designing classical algorithms inspired by quantum approaches.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The short-path quantum algorithm introduced by Hastings (Quantum 2018, 2019) is a variant of adiabatic quantum algorithms that enables an easier worst-case analysis by avoiding the need to control the spectral gap along a long adiabatic path. Dalzell, Pancotti, Campbell, and Brandão (STOC 2023) recently revisited this framework and obtained a clear analysis of the complexity of the short-path algorithm for several classes of constraint satisfaction problems (MAX-$k$-CSPs), leading to quantum algorithms with complexity $2^{(1-c)n/2}$ for some constant $c>0$. This suggested a super-quadratic quantum advantage over classical algorithms. In this work, we identify an explicit classical mechanism underlying a substantial part of this line of work, and show that it leads to clean dequantizations. As a consequence, we obtain classical algorithms that run in time $2^{(1-c')n}$, for some constant $c'>c$, for the same classes of constraint satisfaction problems. This shows that current short-path quantum algorithms for these problems do not achieve a super-quadratic advantage. On the positive side, our results provide a new ``quantum-inspired'' approach to designing classical algorithms for important classes of constraint satisfaction problems.

Problem

• short-path quantum algorithm
• quantum advantage
• constraint satisfaction problems
• dequantization
• MAX-k-CSPs

Innovation

• dequantization
• short-path quantum algorithm
• quantum-inspired classical algorithms
• constraint satisfaction problems
• computational complexity