2025/05/01 by Demirdjian, Reuben, Hogancamp, Thomas, Gunlycke, Daniel · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.00285
Herein, we present a polylogarithmic decomposition method to load the matrix from the linearized 1-dimensional Burgers' equation onto a quantum computer. First, we use the Carleman linearization method to map the nonlinear Burgers' equation into an infinite linear system of equations, which is subsequently truncated to order α. This new finite linear system is then embedded into a larger system of equations with the key property that its matrix can be decomposed into a linear combination of O(log nt + α2log nx) terms for nt time steps and nx spatial grid points. While the terms in this linear combination are not unitary, each is implemented with a simple block encoding and the variational quantuam linear solver (VQLS) routine may be used to obtain a solution. Finally, a complexity analysis of the required VQLS circuits shows that the upper bound of the two-qubit gate depth among all of the block encoded matrices is O(α(log nx)2). This is therefore the first efficient data loading method of a Carleman linearized system.