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arXiv · 1905.07138

Solving systems of linear algebraic equations via unitary transformations on quantum processor of IBM Quantum Experience

S. I. Doronin·E. B. Fel'dman·A. I. Zenchuk
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Abstract

We propose a protocol for solving systems of linear algebraic equations via quantum mechanical methods using the minimal number of qubits. We show that $(M+1)$-qubit system is enough to solve a system of $M$ equations for one of the variables leaving other variables unknown provided that the matrix of a linear system satisfies certain conditions. In this case, the vector of input data (the rhs of a linear system) is encoded into the initial state of the quantum system. This protocol is realized on the 5-qubit superconducting quantum processor of IBM Quantum Experience for particular linear systems of three equations. We also show that the solution of a linear algebraic system can be obtained as the result of a natural evolution of an inhomogeneous spin-1/2 chain in an inhomogeneous external magnetic field with the input data encoded into the initial state of this chain. For instance, using such evolution in a 4-spin chain we solve a system of three equations.

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S. I. Doronin, E. B. Fel'dman, A. I. Zenchuk. 2019-05-17. Solving systems of linear algebraic equations via unitary transformations on quantum processor of IBM Quantum Experience. https://arxiv.org/abs/1905.07138

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