Higher-order spatial discretization reduces qubit count for quantum PDE simulation but does not reduce the number of Trotter steps, so total gate count remains dominated by Trotterization.
For example, {P1, P2}⊗2 is equivalent to {P1, P2} ⊗ {P1, P2}, which is the same as {P1 ⊗ P1, P1 ⊗ P2, P2 ⊗ P1, P2 ⊗ P2}
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High order schemes for solving partial differential equations on a quantum computer
Higher-order spatial discretization reduces qubit count for quantum PDE simulation but does not reduce the number of Trotter steps, so total gate count remains dominated by Trotterization.