### 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 |
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Article number | 115023 |

Journal | New Journal of Physics |

Volume | 14 |

DOIs | |

Publication status | Published - 2012 Nov |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*New Journal of Physics*,

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