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Abstract
 

Matrix inversion is a fundamental task for many disciplines and finding its efficient algorithm is undoubtedly valuable. Recently, quantum algorithms have been developed for matrix inversion that can provide exponential quantum speedup. Here, we propose a new quantum algorithm for matrix inversion assisted with only a single continuous variable (qumode), which greatly simplifies the algorithmic implementation. We give the main procedures for this algorithm, including preparation of qumode resource state, construction of unitary evolution, and projection of the qumode. Theoretical analysis, numeral simulation and physical implementation are also presented. Lastly, we discuss some potential applications, especially on quantum machine learning.

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