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Intell."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product\u2013based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute\u2019s existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product\u2013based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance\u2013based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product\u2013based classifier. The classifiers implement an inner product between<jats:italic>N<\/jats:italic>=\u20092<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>dimension test and train vectors using<jats:italic>n<\/jats:italic>Fredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary number<jats:italic>m<\/jats:italic>of samples that can be classically summed into one input string to effectively execute all test\u2013train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are<jats:inline-formula><jats:alternatives><jats:tex-math>$O(\\log {N})$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:mi>log<\/mml:mi><mml:mi>N<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula>in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). 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