Stabilizer entropy of quantum tetrahedra
Simone Cepollaro, Goffredo Chirco, Gianluca Cuffaro, Gianluca Esposito, Alioscia Hamma
Abstract
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:math> intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts to simulate such models and toward experimental demonstrations of quantum gravity effects. There are, therefore, both a computational and an experimental complexity inherent to this class of models. In this paper, we study this complexity under the lens of (SE). We calculate the SE of the gauge-invariant basis states and its average in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:mo stretchy="false">)</e:mo></e:mrow></e:math>-gauge invariant subspace. We find that the states of definite volume are singled out by the (near) maximal SE and give precise bounds to the verification protocols for experimental demonstrations on available quantum computers. Published by the American Physical Society 2024