Estimation of the ground state of the Heisenberg model using SQD

Quantum spin simulations have been used to study the properties of correlated spin systems and investigate exotic phases of matter such as quantum spin liquids. Whereas exact classical calculations are infeasible due to high computational cost and Monte Carlo or variational methods give inconsistent results, quantum computing is an alternative that may facilitate faster and more accurate calculations. Previous works have explored the Variational Quantum Eigensolver algorithm applied to spin models, but this can lead to large quantum computational overhead. Sample-based Quantum Diagonalization (SQD) is a recently developed hybrid quantum-classical algorithm that refines and expands quantum circuit output to estimate eigenstates. SQD was originally designed for use in electronic structure problems, so we introduce several modifications to make the algorithm symmetry-aware and improve convergence when applied to spin models. We demonstrate the viability of applying this algorithm to spin models by estimating the ground state of a 22-spin antiferromagnetic XXZ Heisenberg chain with an error of 0.006% after 15 iterations. This work illustrates the application of SQD to more diverse problem types and proposes a novel algorithm for studying phase transitions.