Demonstration of a Quantum Circuit Design Methodology for Multiple Regression

Abstract

Multiple linear regression, one of the most fundamental supervised learning algorithms, assumes an imperative role in the field of machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their algorithm could be used to sample the solution of a linear system $Ax=b$ exponentially faster than any existing classical algorithm. Remarkably, any multiple linear regression problem can be reduced to a linear system of equations problem. However, finding a practical and efficient quantum circuit for the quantum algorithm in terms of elementary gate operations is still an open topic. Here we put forward a 7-qubit quantum circuit design, based on an earlier work by Cao et al. [Mol. Phys. 110, 1675 (2012)], to solve a 3-variable regression problem, utilizing only basic quantum gates. Furthermore, we discuss the results of the Qiskit simulation for the circuit and explore certain possible generalizations to the circuit.

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