Purity decay rate in random circuits with different configurations of gates

• URL: http://arxiv.org/abs/2211.13565v1
• Date: Thu, 24 Nov 2022 12:32:07 GMT
• Title: Purity decay rate in random circuits with different configurations of gates
• Authors: Ja\v{s} Bensa and Marko \v{Z}nidari\v{c}
• Abstract summary: We study purity decay -- a measure for bipartite entanglement -- in a chain of $n$ under the action of various geometries. In most circuits, purity decays to its value in two stages: the initial thermodynamically relevant decay up to extensive times is $sim lambda_mathrmeffeff$, with $lambda_mathrmeff$ not necessarily being in the spectrum of the transfer matrix.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study purity decay -- a measure for bipartite entanglement -- in a chain of $n$ qubits under the action of various geometries of nearest-neighbor random 2-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 a brickwall configuration, purity decays to its asymptotic value in two stages: the initial thermodynamically relevant decay persisting up to extensive times is $\sim \lambda_{\mathrm{eff}}^t$ , with $\lambda_{\mathrm{eff}}$ 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 $\lambda_{\mathrm{eff}}$ depends on the location of bipartition boundaries as well on the geometry of applied gates.

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