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An always-on Ising coupling produces evolution during every nominally local pulse, and generally does not commute with the applied $x,y$ Quantum Hamiltonians. A naive product of single-qubit rotations therefore accumulates unwanted conditional phases and can entangle the qubits. Idling is also no longer an identity operation.

For a pulse of duration $\tau$, neglecting the coupling requires $|J_{12}|\tau \ll 1$ in units $\hslash =1$, or $|J_{12}|\tau /\hslash \ll 1$ in ordinary units. For order-one rotation angles, this is the strong-local-drive regime $|B|\gg |J_{12}|$. Large drive amplitude alone does not justify neglect over a long total sequence: the accumulated interaction time or an appropriate error bound must also be small.

If it cannot be neglected, include it in the quantum optimal control model, or refocus it. A $\pi$ pulse $P=R_x^{(1)}(\pi )$ obeys $P(Z\otimes Z)P^{†}=-Z\otimes Z$, giving the ideal Ising spin echoThis cancellation assumes the refocusing pulses are instantaneous relative to $1/|J_{12}|$, or that the coupling during finite pulses is compensated. It explains how fast local controls can suppress the fixed coupling without mistaking it for a controllable zero interaction.