Squiggle data is the numerical output of DNA and RNA sequencing by the Nanopore next generation sequencing platform. Nanopore sequencing offers expanded applications compared to previous sequencing techniques but produces a large amount of data in the form of current reads over time. The analysis of these reads require more complex and computationally intensive algorithms than previous sequencing technologies. The purpose of this study is to investigate in principle the potential of using quantum computers to speed up Nanopore data analysis. Quantum circuits are designed to extract major features of squiggle current reads. The circuits are analyzed theoretically in terms of size and performance. Practical experiments on IBM QX show the limitations of the state of the art quantum computer to tackle real life squiggle data problems. Nevertheless, pre-processing of the squiggle data using the inverse wavelet transform, as experimented and analyzed in this paper as well, reduces the dimensionality of the problem in order to fit a reasonable size quantum computer in the hopefully near future.