Disentangling strategies and entanglement transitions in unitary circuit games with matchgates
AbstractIn 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.Popular summaryQuantum systems consisting of many particles can organize into distinct phases, in the same way that water can be ice, liquid, or steam depending on temperature. In quantum matter, a key quantity that distinguishes phases is entanglement: the degree to which the individual particles are correlated with one another. In a highly entangled phase, knowing the state of one part of the system reveals information about distant parts; in a weakly entangled phase, correlations remain mostly local. A natural question is: which feature determines whether entanglement builds up or is suppressed in a system? One way to probe this is through "unitary circuit games." A quantum circuit is a sequence of elementary operations, so-calle
