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 |
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| Keywords: | quantum mechanics, statistical mechanics, quantum circuits, quantum gates, quantum information theory, quantum statistical mechanics, quantum information, science and technology, statistical physics, thermodynamics |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FMF - Faculty of Mathematics and Physics
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| Publication status: | Published |
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| Publication version: | Author Accepted Manuscript |
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| Year: | 2023 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 107, iss. 2, art. 022604 |
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| PID: | 20.500.12556/RUL-155058  |
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| UDC: | 536.93 |
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| ISSN on article: | 2469-9926 |
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| DOI: | 10.1103/PhysRevA.107.022604 |
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| COBISS.SI-ID: | 188884995 |
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| Publication date in RUL: | 18.03.2024 |
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| Views: | 472 |
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| Downloads: | 568 |
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