Preparing 100-site gapped ground states of the XXZ model and the bond-alternating Heisenberg model on quantum hardware

Preparing ground states on quantum computers is a foundational task in the study of many body quantum physics. Despite this, quantum algorithms for state preparation often produce circuits which have low fidelity or high depth. In this work, we use tensor-network optimisation of shallow circuits to prepare gapped ground states of large spin chains to high accuracy on quantum hardware. We first demonstrate this for the 100-site XXZ model, preparing a ground state on IBM quantum hardware closer to the antiferromagnetic-XY phase boundary than previously achieved. We subsequently consider the 100-site spin-½ bond-alternating Heisenberg chain. We find that the optimised circuits are able to prepare ground states in the symmetry-protected topological phase to high accuracy with as low as 15 CNOT depth. This enables the accurate measurement of observables, such as single-site spin components, two-point correlations, and energy. Importantly, the circuits preserve the signature non-local string order, despite their approximate nature. Looking ahead, this methodology offers a scalable route to high-fidelity, low-depth ground state preparation, laying the groundwork for simulating long-time quench dynamics, exploring classically intractable regimes, on early fault-tolerant quantum hardware.