Recently there has been considerable interest in the topic of eigenstate preparation. The question is whether selected eigenstates (or perhaps all eigenstates) of certain models can be prepared efficiently on a quantum computer. Efficient means that the number of gates needed (and possibly the number of auxiliary qubits needed) scales only polynomially with the number of particles and the length of the spin chain. Integrable models have relatively “simple” eigenstates, as compared to those of chaotic models. This motivated the idea/conjecture that eigenstates of integrable models should not be complex from the quantumcomputation point of view. However, the question is very far from obvious. In this talk we review recent attempts and contributions, including work of the speaker[1, 2]. We will explain that the question of eigenstate preparation and quantum computational complexity in integrable models is not yet settled, and it is an active area of research today.

 

[1]: PRX Quantum 6, 030316 (2025)

[2]: SciPost Phys. 18, 187 (2025)