2018/05/11 by Koji Hashimoto, Norihiro Iizuka, Sotaro Sugishita · 3 citations
Mathematics · Physics and Astronomy · #Algorithm #Basis (linear algebra) #Black Holes and Theoretical Physics #Computational complexity theory #Cosmology and Gravitation Theories #Discrete mathematics #Geometry #Hilbert space #Holography #Invariant (physics) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #State (computer science) #hep-th
paper · pdf · doi:10.1103/physrevd.98.046002
published as Phys. Rev. D 98, 046002 (2018) · 7 pages
arxiv created 2018/05/11 · openalex publication_date 2018/08/06 · arxiv updated 2018/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this minimality, it satisfies the triangle inequality and can be regarded as a (discrete version of) distance in the Hilbert space. However, we show a no-go theorem that any basis-independent distance cannot reproduce the behavior of the holographic complexity. Therefore, if holographic complexity is dual to a distance in the Hilbert space, it should be basis dependent; i.e., it is not invariant under a change of the basis of the Hilbert space.