### Abstract

Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an N-dimensional linear equation in O(logN) time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is 2×2 using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.

Original language | English |
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Article number | 022313 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 89 |

Issue number | 2 |

DOIs | |

Publication status | Published - 12 Feb 2014 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*89*(2), [022313]. https://doi.org/10.1103/PhysRevA.89.022313

**Experimental realization of quantum algorithm for solving linear systems of equations.** / Pan, Jian; Cao, Yudong; Yao, Xiwei; Li, Zhaokai; Ju, Chenyong; Chen, Hongwei; Peng, Xinhua; Kais, Sabre; Du, Jiangfeng.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 89, no. 2, 022313. https://doi.org/10.1103/PhysRevA.89.022313

}

TY - JOUR

T1 - Experimental realization of quantum algorithm for solving linear systems of equations

AU - Pan, Jian

AU - Cao, Yudong

AU - Yao, Xiwei

AU - Li, Zhaokai

AU - Ju, Chenyong

AU - Chen, Hongwei

AU - Peng, Xinhua

AU - Kais, Sabre

AU - Du, Jiangfeng

PY - 2014/2/12

Y1 - 2014/2/12

N2 - Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an N-dimensional linear equation in O(logN) time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is 2×2 using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.

AB - Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an N-dimensional linear equation in O(logN) time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is 2×2 using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.

UR - http://www.scopus.com/inward/record.url?scp=84894477623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894477623&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.89.022313

DO - 10.1103/PhysRevA.89.022313

M3 - Article

AN - SCOPUS:84894477623

VL - 89

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022313

ER -