Purity decay rate in random circuits with different configurations of gatesBensa, Jaš (Avtor) Žnidarič, Marko (Avtor) quantum mechanicsstatistical mechanicsquantum circuitsquantum gatesquantum information theoryquantum statistical mechanicsquantum informationscience and technologystatistical physicsthermodynamicsWe 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.20232024-03-18 13:12:02Članek v reviji155058sl