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

TL;DR

This paper demonstrates how to experimentally identify and distinguish mixed-state phases in a quantum system using Renyi correlators and quantum error correction on a quantum computer, highlighting a new approach for quantum phase characterization.

Contribution

It introduces a method combining shadow tomography, Renyi correlators, and variational decoding to probe and differentiate mixed-state phases on a quantum computer.

Findings

Renyi correlators show distinct decay behaviors in different phases.

Shallow quantum circuits can effectively distinguish phases via decoding fidelity.

The approach provides a proof of concept for quantum simulation of mixed-state phases.

Abstract

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 observe a newly proposed Renyi correlator in two distinct phases: one exhibiting power-law decay and the other long-ranged. Second, we investigate the decoding fidelity of the associated quantum error-correcting code using a variational quantum circuit, and we find that a shallow circuit is sufficient to distinguish the above-mentioned two mixed-state phases through the decoding performance quantified by entanglement fidelity. Our work is a proof of concept for the quantum simulation and characterization of mixed-state phases.