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.
, xn) is expressed as x = Pn j=1 xj2n−j
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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.