Real Postselection In Quantum Imaginary Time

Postselection is the power to amplify the probability of any quantum measurement outcome with non-zero probability of occurrence. If such a power was available to us without exponential in system size complexity (number of steps) of performing this task, then it would imply that NP is in BQP. We do not expect this to be true, however, we can expect to find nontrivial states (where non zero probabilities are not all 1/poly(n)) where we have the power to postselect efficiently. We propose low cluster-correlation states and Quantum Imaginary Time Evolution (QITE) method as viable candidates for this task. As a proof of concept, we provide evidence that we only require poly(n) runs of the measured random circuits to experimentally infer if the system is in the area law phase or not. Priori to this work, such a procedure was only available to experimentally observe if the system was in the volume law phase of measurement induced criticality. This work opens up novel application of QITE as a probability amplification scheme to postselect quantum states with low cluster correlations.