Purity decay rate in random circuits with different configurations of gates

Abstract

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 $\sim {\lambda }_{\mathrm{eff}}^t$, 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 as on the geometry of applied gates.

version 2

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Cited by in corpus (6)

• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Two-step relaxation in local many-body Floquet systems
• Theory of Irreversibility in Quantum Many-Body Systems
• Boom and bust cycles due to pseudospectra of matrices with unimodular spectra