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Phys Rev Lett. 2013 Jun 7;110(23):230501. Epub 2013 Jun 6.

Experimental quantum computing to solve systems of linear equations.

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Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Center for Quantum Information and Quantum Control, Department of Electrical and Computer Engineering, and Department of Physics, University of Toronto, Toronto M5S 3G4, Canada.
Centre for Quantum Technologies, National University of Singapore, Singapore 117543 and Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China.


Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

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