Dequantizing Short-Path Quantum Algorithms

• URL: http://arxiv.org/abs/2604.12131v1
• Date: Mon, 13 Apr 2026 23:31:53 GMT
• Title: Dequantizing Short-Path Quantum Algorithms
• Abstract summary: Short-path quantum algorithm is a variant of adiabatic quantum algorithms.<n>We show that short-path quantum algorithms for constraint satisfaction problems do not achieve a super-quadratic advantage.
• Score: 1.1602089225841632
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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