Many thanks to my awesome co-author Lukasz Cincio for this fun project

Concluding thread with a TL;DR

... and on Fault-Tolerant hardware, with similar reductions in required T-gates compared to Trotterized circuits.

More pressingly, we show that our optimised circuits can realise the time evolution unitary e^{-iHt} with shallower circuits than all equivalent depth Trotterizations.

This helps simulations on NISQ hardware, with reduced CNOT depths required to reach a target error rate, ...

Among a range of applications, we show that infinite ground states can be prepared to high accuracy

All circuits are generated through variational optimization of infinite layers, to maximise overlap with a target state.

Our unified approach to this compilation is a cost function based on 'local fidelities' between states, using operations on mixed transfer matrices.

🎹 We exploit translation invariance, a symmetry found in many physical systems

😅 Circuits describing these systems are vastly simpler, reducing optimization complexity

♾️ Our compilation is based on infinite MPS, creating efficient circuits ready to upload to the QC to access higher entanglement

📝 New paper - "Learning Circuits with Infinite Tensor Networks" ⚛️

Check out our latest work to find out how classical computers (via tensor networks) can support Hamiltonian simulation, in the thermodynamic limit, on both NISQ + Fault-Tolerant quantum computers

Paper link: arxiv.org/abs/2506.02105