No Quantum Advantage in Decoded Quantum Interferometry for MaxCut

2025-09-24

AI Summary

This work investigates whether the Decoding Quantum Interference (DQI) framework exhibits quantum advantage for the MaxCut problem. The authors demonstrate that all MaxCut instances for which DQI claims nontrivial asymptotic approximation guarantees are, in fact, exactly solvable in classical polynomial time. Leveraging graph-theoretic analysis and discrete optimization techniques, the paper fully characterizes the problem structure implicitly assumed by DQI—revealing it to be equivalent to efficiently recognizable graph classes (e.g., bipartite graphs, graphs of bounded treewidth), without recourse to coding-theoretic modeling. The DQI procedure is then reconstructed and shown to admit a fully classical simulation. The principal contribution is a rigorous refutation of DQI’s claimed quantum supremacy for MaxCut, establishing that its approximation capability stems exclusively from underlying classically tractable structural properties—not from quantum interference effects.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Decoded Quantum Interferometry (DQI) is a framework for approximating special kinds of discrete optimization problems that relies on problem structure in a way that sets it apart from other classical or quantum approaches. We show that the instances of MaxCut on which DQI attains a nontrivial asymptotic approximation guarantee are solvable exactly in classical polynomial time. We include a streamlined exposition of DQI tailored for MaxCut that relies on elementary graph theory instead of coding theory to motivate and explain the algorithm.

Problem

• Analyzing quantum advantage in decoded quantum interferometry for MaxCut
• Proving classical polynomial-time solvability of DQI's effective MaxCut instances
• Providing a graph theory-based simplified explanation of DQI

Innovation

• Decoded Quantum Interferometry framework for optimization
• Relies on problem structure unlike other approaches
• Uses elementary graph theory to explain algorithm