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Quantum Circuit Design Gate Engineering

The complexity of semidefinite programs for testing k-block-positivity

arXiv
Authors: Qian Chen, Benoît Collins

Year

2026

Paper ID

3285

Status

Preprint

Abstract Read

~2 min

Abstract Words

65

Citations

N/A

Abstract

We extend \cite{chen2025srkbp} by analyzing the complexity of the k-block-positivity testing algorithm. In this paper, we investigate a symmetry reduction scheme based on rectangular shaped Young diagrams. Connecting the complexity to the dimensions of irreducible representations of U(d), we derive an explicit formula for the complexity, which also clarifies why the semidefinite program hierarchy collapses in the k=d case.

Why This Paper Matters

  • This paper contributes to the Quantum Circuit Design & Gate Engineering research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • We extend citechen2025srkbp by analyzing the complexity of the k-block-positivity testing algorithm.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.19159 [2] arXiv https://arxiv.org/abs/2601.19159 [3] Publisher https://arxiv.org/abs/2601.19159

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