title: Experimental quantum computing to solve systems of linear equations.
abstract: 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.
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: X-D
authors.initials: XD
authors.lastname: Cai
authors.affiliation: Center for Quantum Information and Quantum Control, Department of Electrical and Computer Engineering, and Department of Physics, University of Toronto, Toronto M5S 3G4, Canada.
authors.forename: C
authors.initials: C
authors.lastname: Weedbrook
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Z-E
authors.initials: ZE
authors.lastname: Su
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: M-C
authors.initials: MC
authors.lastname: Chen
authors.affiliation: 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.
authors.forename: Mile
authors.initials: M
authors.lastname: Gu
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: M-J
authors.initials: MJ
authors.lastname: Zhu
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Li
authors.initials: L
authors.lastname: Li
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Nai-Le
authors.initials: NL
authors.lastname: Liu
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Chao-Yang
authors.initials: CY
authors.lastname: Lu
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Jian-Wei
authors.initials: JW
authors.lastname: Pan