Homological Invariants of Pauli Stabilizer Codes

• DOI: 10.1007/s00220-024-04991-y
• Publication Date: 2024-05-08T21:01:50Z
• Authors: Blazej Ruba; Bowen Yang
• Keywords: Complex system; Stabilizer (aeronautics); Pauli exclusion principle

Abstract We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series invariants called charge modules. describe their properties and physical meaning. The most complete results are obtained for whose modules have Krull dimension zero. This condition is interpreted as mobility excitations. show that it always satisfied translation 2D unique ground state in infinite volume, which was previously known only the case prime qudit dimension. For all excitations mobile construct p -dimensional excitation $$(D-p-1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>-</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> -form symmetry every element -th module. Moreover, braiding pairing between complementary degrees. discuss examples illustrate how can be computed practice.