Robust preparation of ground state phases under noisy imaginary time evolution

TL;DR

This paper investigates the robustness of imaginary time evolution (ITE) in preparing ground states under noise, showing that phases are preserved if noise respects certain symmetries, with implications for noisy quantum hardware.

Contribution

It demonstrates that symmetry-preserving noise does not destroy the phase of states prepared by ITE, providing insights into noise resilience in quantum state preparation.

Findings

Ground state phases persist under symmetry-preserving noise.

Phase transition remains intact with weak or average symmetry-preserving noise.

Analysis uses an effective Hamiltonian in a doubled Hilbert space.

Abstract

Non-unitary state preparation protocols such as imaginary time evolution (ITE) offer substantial advantages relative to unitary ones, including the ability to prepare certain long-range correlated states more efficiently. Here, we ask whether such protocols are also robust to noise arising due to coupling to the environment. We consider a non-unitary ITE "circuit" subjected to a variety of noise models and investigate whether the resulting steady state remains in the same phase as the target state of the ITE at finite noise strength. Taking the one-dimensional quantum Ising model as a concrete example, we find that the ground state order and associated phase transition persist in the presence of noise, provided the noise does not explicitly break the symmetry that protects the phase transition. That is, the noise must possess the protecting symmetry in a weak (or average) form. Our analysis is facilitated by a mapping to an effective Hamiltonian picture in a doubled Hilbert space. We discuss possible implications of these findings for quantum simulation on noisy quantum hardware.