Error-Suppressed Quantum Simulation of Programmable Spin Hamiltonians

Trapped ions can simulate spin-spin Hamiltonians such as the Ising model by engineering their coupling to phonon modes. However, in most experiments the interaction is limited to specific coupling profiles (e.g., power-law or exponential), and the fidelity is constrained by residual spin-phonon entanglement. Here, we introduce a pulse-shaping strategy for the driving fields that enables programmable implementation of a broad class of Ising interaction graphs while suppressing spin-phonon coupling throughout the entire evolution, rather than only at the end as in standard digital protocols. This approach reduces both residual phonon errors and errors arising from nested commutators in the time evolution, resulting in more than an order-of-magnitude improvement in the fidelity of simulating the transverse-field Ising model. The technique is broadly applicable to trapped-ion systems and potentially to other quantum simulation platforms.