Quantum Support Vector Machine without Iteration
- URL: http://arxiv.org/abs/2206.00909v1
- Date: Thu, 2 Jun 2022 07:57:39 GMT
- Title: Quantum Support Vector Machine without Iteration
- Authors: Rui Zhang, Jian Wang, Nan Jiang, Zichen Wang
- Abstract summary: This paper proposes a quantum support vector machine (LS-QSVM) based on the generalized quantum amplitude estimation (AE-QSVM)
Experiments demonstrate that AE-QSVM is advantageous in terms of training matrix, the number of iterations, space complexity, and time complexity.
- Score: 17.384061512750158
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum algorithms can enhance machine learning in different aspects. In
2014, Rebentrost $et~al.$ constructed a least squares quantum support vector
machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the
classification. However, as the output states of a previous test cannot be
reused for a new test in the Swap Test, the quantum algorithm LS-QSVM has to be
repeated in preparing qubits, manipulating operations, and carrying out the
measurement. This paper proposes a QSVM based on the generalized quantum
amplitude estimation (AE-QSVM) which gets rid of the constraint of repetitive
processes and saves the quantum resources. At first, AE-QSVM is trained by
using the quantum singular value decomposition. Then, a query sample is
classified by using the generalized quantum amplitude estimation in which high
accuracy can be achieved by adding auxiliary qubits instead of repeating the
algorithm. The complexity of AE-QSVM is reduced to
$O(\kappa^{3}\varepsilon^{-3}(log(mn)+1))$ with an accuracy $\varepsilon$,
where $m$ is the number of training vectors, $n$ is the dimension of the
feature space, and $\kappa$ is the condition number. Experiments demonstrate
that AE-QSVM is advantageous in terms of training matrix, the number of
iterations, space complexity, and time complexity.
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