Entanglement scaling beyond product-formula simulation

Determine whether the entanglement resource scaling achieved by the repeat-until-success protocol for product-formula simulation extends to other Hamiltonian-simulation methods, including linear combinations of unitaries, quantum signal processing, and quantum singular value transformation.

Background

The main results establish linear-in-time entanglement cost, independent of Trotter error, for fixed-order product-formula simulations whose nonlocal rotations are implemented using the repeat-until-success protocol. The paper does not establish whether comparable scaling holds for alternative simulation paradigms.

The authors explicitly identify this extension as open for methods based on linear combinations of unitaries, quantum signal processing, and quantum singular value transformation.