Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation

TL;DR

This paper demonstrates efficient quantum circuit methods for preparing eigenstates of certain integrable spin chains, including those with Hilbert space fragmentation, using error-mitigated simulations up to 13 qubits.

Contribution

It introduces explicit quantum circuits for eigenstate preparation in an interacting integrable model with Hilbert space fragmentation, extending Bethe ansatz reformulation to open boundaries.

Findings

Polynomial-depth circuits for eigenstate preparation in selected models

Successful error-mitigated simulations with up to 13 qubits

Extension of Bethe ansatz reformulation to open boundary conditions

Abstract

We consider the preparation of all the eigenstates of spin chains using quantum circuits. It is known that generic eigenstates of free-fermionic spin chains can be prepared with circuits whose depth grows only polynomially with the length of the chain and the number of particles. We show that the polynomial growth is also achievable for selected interacting models where the interaction between the particles is sufficiently simple. Our working example is the folded XXZ model, an integrable spin chain that exhibits Hilbert space fragmentation. We present the explicit quantum circuits that prepare arbitrary eigenstates of this model on an open chain efficiently. We perform error-mitigated noisy simulations with circuits of up to 13 qubits and different connectivities between qubits, achieving a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit from closed to open boundary conditions.