### Abstract

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error , arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log ) or O(log log ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.

Original language | English |
---|---|

Article number | 115023 |

Journal | New Journal of Physics |

Volume | 14 |

DOIs | |

Publication status | Published - 2012 Nov |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*14*, [115023]. https://doi.org/10.1088/1367-2630/14/11/115023

**Faster quantum chemistry simulation on fault-tolerant quantum computers.** / Jones, N. Cody; Whitfield, James D.; McMahon, Peter L.; Yung, Man Hong; Van Meter, Rodney D; Aspuru-Guzik, Alán; Yamamoto, Yoshihisa.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 14, 115023. https://doi.org/10.1088/1367-2630/14/11/115023

}

TY - JOUR

T1 - Faster quantum chemistry simulation on fault-tolerant quantum computers

AU - Jones, N. Cody

AU - Whitfield, James D.

AU - McMahon, Peter L.

AU - Yung, Man Hong

AU - Van Meter, Rodney D

AU - Aspuru-Guzik, Alán

AU - Yamamoto, Yoshihisa

PY - 2012/11

Y1 - 2012/11

N2 - Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error , arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log ) or O(log log ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.

AB - Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error , arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log ) or O(log log ); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.

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U2 - 10.1088/1367-2630/14/11/115023

DO - 10.1088/1367-2630/14/11/115023

M3 - Article

VL - 14

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 115023

ER -