Purity decay rate in random circuits with different configurations of gates

Bensa, Jaš (author), Žnidarič, Marko (author)

We study purity decay—a measure of bipartite entanglement—in a chain of n qubits under the action of various geometries of nearest-neighbor random two-site unitary gates. We use a Markov chain description of average purity evolution, using further reduction to obtain a transfer matrix of only polynomial dimension in n. In most circuits, an exception being the brick-wall configuration, purity decays to its asymptotic value in two stages: the initial thermodynamically relevant decay persisting up to extensive times is $\sim \lambda^t_{eff}$, with $\lambda_{eff}$ not necessarily being in the spectrum of the transfer matrix, while the ultimate asymptotic decay is given by the second largest eigenvalue $\lambda_2$ of the transfer matrix. The effective rate $\lambda_{eff}$ depends on the location of bipartition boundaries as well as on the geometry of applied gates.

• Language: English
• Keywords: quantum mechanics, statistical mechanics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication version: Author Accepted Manuscript
• Publication date: 06.02.2023
• Year: 2023
• Number of pages: Str. 022604-1-022604-13
• Numbering: Vol. 107, iss. 2
• PID: 20.500.12556/RUL-155058
• UDC: 536.93
• ISSN on article: 2469-9926
• DOI: 10.1103/PhysRevA.107.022604
• COBISS.SI-ID: 188884995
• Publication date in RUL: 18.03.2024

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9926
• COBISS.SI-ID: 2996836

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, statistična mehanika