Clustering Algorithm for Predicting Quantum States in a Quantum Computer
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Date
2021-05
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The Ohio State University
Abstract
Quantum state tomography refers to the process of estimating the density matrix of an unknown system after obtaining data through a series of quantum measurements. Quantum state tomography can be divided into two processes: quantum measurement and reconstruction algorithm. From these two processes, different schemes can be designed, and they also have their own advantages and disadvantages. At the same time, quantum tomography is mainly concerned with two factors: estimation accuracy and complexity. High-precision quantum tomography is a necessary condition for quantum computing and other quantum technologies, and the scarcity of quantum resources forces us to find more effective methods to reduce estimation errors. The complexity problem of quantum tomography grows with the dimensionality of the quantum system. I simulate the behavior of a linear optics quantum computing circuit that performs the quantum Fourier transform. We investigated the possibility of using k-means clustering algorithm to predict the output of the quantum computer and compare its performance with the conditional generative adversarial network (CGAN), shadow tomography, maximum likelihood estimation. Using this simulated data, I apply the various algorithms to the order-finding problem to determine the trade-off between the required number of measurements and the accuracy. The result shows that k-means clustering can take a polynomial number of samples to access the result of the order-finding problem with more than 90 percent accuracy. The comparison of all four methods is analyzed.