arXiv subjects

Shi-Kang Sun

Publications and source records attributed to Shi-Kang Sun.

2 recordsLinked to original sources

arXiv2025

Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates

We study quantum circuits with gates composed randomly of identity operators, projectors, or a kind of $R$ matrices which satisfy the Yang-Baxter equation and are unitary and dual-unitary. This enables us to translate the quantum circuit into a topological object with distinguished overcrossings and undercrossings. The circuit corresponds to a classical loop model and is post-selection free when an overcrossing and an undercrossing coincide. The entanglement entropy between the final state and initial state is given by the spanning number of the classical model, and they share the same phase diagram. Whenever an overcrossing and undercrossing differ, the circuit extends beyond the classical model. Considering a specific case with $R$ matrices randomly replaced by SWAP gates, we demonstrate that the topological effect originating from worldline braiding dominates, and only the area-law phase remains in the thermodynamic limit, regardless of how small the replacement probability is. We also find evidence of an altered phase diagram for non-Clifford cases.

quant-ph↗

arXiv2024

Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics

We explicitly construct unique non-equilibrium steady state (NESS) of Lindblad master equation characterized by a Gibbs ensemble $\rho_{\text{NESS}} \propto e^{-\beta \tilde{H}}$, where the effective hamiltonian $\tilde{H}$ is an element in the center of the commutant algebra $\mathcal{C}$ of the original hamiltonian. Specifically, if $\mathcal{C}$ is Abelian, then $\tilde{H}$ consists only of $U(1)$ conserved charges of the original Hamiltonian. When the original Hamiltonian has multiple charges, it is possible to couple them with bathes at different temperature respectively, but still leads to an equilibrium state. Multiple steady states arise if the number of bathes is less than the number of charges. To access the Gibbs NESS, the jump operators need to be properly chosen to fulfill quantum detailed balance condition (qDBC). These jump operators are ladder operators for $\tilde{H}$ and jump process they generate form a vertex-weighted directed acyclic graph (wDAG). By studying the XX model and Fredkin model, we showcase how the Gibbs state emerges as an equilibrium steady state.

quant-ph↗