标题： 通过匹配门的单位电路博弈中的解缠策略和纠缠转变 显示英文标题

标题： Disentangling strategies and entanglement transitions in unitary circuit games with matchgates

摘要： 在幺正电路博弈中，两个竞争方，“纠缠者”和“解纠缠者”，可以在一个量子多体系统中引发纠缠相变。这种转变发生在解纠缠者作用的某个速率处。我们将在匹配门动力学的背景下分析此类博弈，这等价于非相互作用费米子的演化。我们首先研究费米子高斯态（FGS）的一般纠缠性质。我们引入一种使用最小匹配门电路表示FGS的方法，该电路能够制备该状态，并基于广义的杨-巴克斯特关系推导出一个算法，用于在应用幺正操作时更新此表示。这种表示使我们能够定义一种自然的解纠缠过程，减少电路中的门数，从而降低系统中的纠缠度。然后，我们探讨了不同的解纠缠策略，并在两种不同场景下研究了幺正电路博弈：带有编织门，即 Clifford 门和匹配门的交集，以及带有通用匹配门的情况。对于每个模型，我们观察到定性不同的纠缠相变，我们通过数值和解析方法对其进行了表征。 显示英文摘要

摘要： In unitary circuit games, two competing parties, an "entangler" and a "disentangler", can induce an entanglement phase transition in a quantum many-body system. The transition occurs at a certain rate at which the disentangler acts. We analyze such games within the context of matchgate dynamics, which equivalently corresponds to evolutions of non-interacting fermions. We first investigate general entanglement properties of fermionic Gaussian states (FGS). We introduce a representation of FGS using a minimal matchgate circuit capable of preparing the state and derive an algorithm based on a generalized Yang-Baxter relation for updating this representation as unitary operations are applied. This representation enables us to define a natural disentangling procedure that reduces the number of gates in the circuit, thereby decreasing the entanglement contained in the system. We then explore different strategies to disentangle the systems and study the unitary circuit game in two different scenarios: with braiding gates, i.e., the intersection of Clifford gates and matchgates, and with generic matchgates. For each model, we observe qualitatively different entanglement transitions, which we characterize both numerically and analytically.