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A reliable determination of probability density functions from data samplesis still a relevant topic in scientific applications. In this work weinvestigate the possibility of defining an algorithm for density functionestimation using adiabatic quantum computing. Starting from a sample of aone-dimensional distribution, we define a classical-to-quantum data embeddingprocedure which maps the empirical cumulative distribution function of thesample into time dependent Hamiltonian using adiabatic quantum evolution. Theobtained Hamiltonian is then projected into a quantum circuit using the timeevolution operator. Finally, the probability density function of the sample isobtained using quantum hardware differentiation through the parameter shiftrule algorithm. We present successful numerical results for predefined knowndistributions and high-energy physics Monte Carlo simulation samples.

Determining probability density functions with adiabatic quantum computing