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Ilia Lazarev
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fix latex style
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manuscript.tex

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@@ -406,8 +406,8 @@ \subsection{Optimized quantum scheme for Hamming distance calculation}
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From those amplitudes estimations we are able to plot the distance matrix between two data sets of binary vectors.
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The probability amplitude of the ancilla qubit outcomes captures the exact Hamming distance as the result of the preprocessing function.
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There are two possible outcomes of measurement of the ancilla qubit, each has own probability amplitude and own interpretation of that amplitude.
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For instance, for the |0> outcome, the larger the amplitude the smaller the Hamming distance,
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and for the |1> outcome it is the other way around, magnitude of the amplitude of that outcome is proportional to the Hamming distance.
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For instance, for the \left| 0 \right\rangle outcome, the larger the amplitude the smaller the Hamming distance,
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and for the \left| 1 \right\rangle outcome it is the other way around, magnitude of the amplitude of that outcome is proportional to the Hamming distance.
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Measuring the Hamming distance of a particular pair of input vectors $\left| x_i \right\rangle$ and cluster vector $\left| y_j \right\rangle$ consists of extracting the relevant amplitude from the subspace that those states form,
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this can be done using the following projection operator

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