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Proceedings of the Russian higher school Academy of sciences

3JJ Q-bit state identification using the maximum-likelihood method

Vostretsov Aleksey, Krivetsky Andrey, Radchenko Sergey, Dmitriy K. Pitsun

Published Sep 21, 2015• 0 citations
Publisher
DOI
10.17212/1727-2769-2015-3-39-49

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Identifying an unknown unitary quantum process is a fundamental task in the development of quantum technology. In this paper, we propose an efficient identification algorithm for estimating unitary processes. In the method, input pure states are used and a fast quantum state tomography algorithm is developed to reconstruct the output states. Then the information of the output states is used to estimate the unitary process. The identification algorithm has computational complexity O(d3) for a d-dimensional system. Numerical results show that the proposed identification algorithm is much more efficient than the maximum likelihood estimation method and works well for input mixed states with high purity. An analytical upper bound for the identification error is also provided, and numerical simulations and experimental results on quantum optical systems verify the theoretical results.
Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.