Offline recovery of magic and entanglement from noisy Pauli product states

The dependence of quantum algorithms on state fidelity is difficult to characterize analytically and is best explored experimentally as hardware scales and noisy simulations become intractable. While low fidelity states are often disregarded, they may still retain valuable information, as long as their dominant eigenvector approximates the target state. Through classical purification, we demonstrate the ability to recover resources specific to quantum computing such as magic and entanglement from noisy states generated by Pauli product formulas, which are common subroutines of many quantum algorithms. Additionally we show that the fidelity of the purified state is dependent on both the magnitude and order in which magic and entanglement are generated, which can be used to inform the order of operators within an ansatz. Consistent across simulation and experiment on IonQ's Aria quantum device, correlations within a state are found to be much more robust to noise than magic, and we show the advantage of designing algorithms targeting these low error states. This study uses quantum informatic tools for analyzing and optimizing quantum algorithms in a noisy framework.