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In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled (LRE) states lead to phases of matter which are stable to gate imperfections. Here we show that such gate imperfections effectively convert projective into weak measurements and that, in certain cases, long-range entanglement persists, even in the presence of weak measurements and gives rise to novel forms of quantum criticality. We demonstrate this explicitly for preparing the two-dimensional (2D) GHZ cat state and the three-dimensional (3D) toric code as minimal instances. In contrast to previous studies on measurement-induced phases and transitions, our circuit of gates and measurements is deterministic; the only randomness is in the measurement outcomes. We show how the randomness in these weak measurements allows us to track the solvable Nishimori line of the random-bond Ising model, rigorously establishing the stability of the glassy LRE states in two and three spatial dimensions. Away from this exactly solvable construction, we use hybrid tensor network and Monte Carlo simulations to obtain a non-zero Edwards-Anderson order parameter as an indicator of long-range entanglement in the 2D scenario. We argue that our protocol admits a natural implementation in existing quantum computing architectures, requiring only a depth-3 circuit on IBM's heavy-hexagon transmon chips.

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Guo-Yi Zhu
Seminar Room 0.03, ETP and zoom (https://uni-koeln.zoom.us/j/96646818958 )
Contact: Lasse Gresista