TBNQuantum
On the Role of Problem Structure in Single-Layer QAOA
Publication: quant-ph updates on arXiv.org
Author: Guilherme Adamatti Bridi, Franklin de Lima Marquezino, Andris Ambainis
Source published: 23/10/2026, 04:00:00 UTC
Briefing created: 23/10/2026, 04:21:45 UTC
Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 23/10/2026, 04:13:25 UTC.
Briefings
This article identifies a mathematical object encoding problem structure in single-layer QAOA via a joint probability distribution from the target state amplitude. It establishes a mean-max non-separation bound relating parameter-averaged measurement probabilities to variational maxima, enabling characterization of exponential amplification scaling for NPO-PB problems with polynomially many mixer eigenvalues. The authors derive an exact expression for this probability as a matrix inner product involving structural and mixer dynamics objects, validated through transverse field and Grover mixer examples.
Key points
- The study identifies a mathematical object encoding problem structure in single-layer QAOA via a joint probability distribution derived from the target state amplitude.
- A mean-max non-separation bound relates parameter-averaged measurement probabilities to variational maxima, enabling characterization of exponential amplification scaling for NPO-PB problems with polynomially many mixer eigenvalues.
Context
Problem structure is a key factor influencing QAOA performance but lacks precise mathematical characterization. This work provides a formal framework to quantify available problem structure and identify conditions for exponential amplification.
Limitations
Results apply to single-layer QAOA and NPO-PB problems with polynomially many distinct mixer eigenvalues. The study uses analytically tractable examples but does not claim general applicability to all problem classes or specific hardware implementations.
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