Probing mixed-state phases on a quantum computer via Renyi correlators and variational decoding

Recent advances have defined nontrivial phases of matter in open quantum systems such as many-body quantum states subject to environmental noise. In this work, we experimentally probe and characterize mixed-state phases on Quantinuum's H1 quantum computer using two measures: Renyi correlators and the coding performance of a quantum error-correcting code associated with the phase. As a concrete example, we probe the low-energy states of the critical transverse field Ising model under different dephasing noise channels. First, we employ shadow tomography to extract a newly proposed Renyi correlator in two distinct phases obtained by applying two different channels, observing one with faster decay and the other with slower decay. Second, we investigate the decoding fidelity of the associated quantum error-correcting code using a variational quantum circuit. We find that a shallow circuit of depth-3 is sufficient to distinguish the above-mentioned two mixed-state phases, up to L = 24. Experimentally, we observe this distinction for system sizes up to L = 8 with a depth-1 decoder. Our work is a proof of concept for the quantum simulation and characterization of mixed-state phases.