Non-unitary dynamics in N-qubit quantum circuits and its link with complex temperature statistical mechanics of the Ising Model*

This talk primarily focuses on the relationship between non-unitary dynamics of a N-qubit quantum circuits with measurement and the spin-spin correlations of the N-leg Ising ladder at complex temperatures. In the large N-limit of the Ising ladder, we will show that there is a finite region in the complex fugacity plane in which spin-spin correlations exhibit incommensurate oscillatory (quasi)long range correlations. We argue that these are due to 'partial unitarity' of an associated N-qubit quantum circuit, whereby some coherence is retained in the long time limit. We also show that there exists special points in the complex fugacity plane where full unitarity is recovered.