Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation

This is the authors' abstract. We don't add key points for this paper.

We demonstrate that eigenstates of selected interacting spin chains can be efficiently prepared using quantum circuits with polynomial depth in system size and particle number. While this is well established for free-fermionic spin chains, we extend this result to the folded <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>X</a:mi><a:mi>X</a:mi><a:mi>Z</a:mi></a:math> model, an integrable rigid-rod deformation of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>X</c:mi><c:mi>X</c:mi></c:math> model with simple interactions that exhibits Hilbert space fragmentation. We construct explicit quantum circuits that efficiently prepare arbitrary eigenstates of this model on an open chain. Error-mitigated noisy simulations with up to 13 qubits and various qubit connectivities achieve a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit to open boundary conditions.