Faster quantum chemistry simulation on fault-tolerant quantum computers

N. Cody Jones, James D. Whitfield, Peter L. McMahon, Man Hong Yung, Rodney Van Meter, Alán Aspuru-Guzik, Yoshihisa Yamamoto

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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 languageEnglish
Article number115023
JournalNew Journal of Physics
Volume14
DOIs
Publication statusPublished - 2012 Nov 1

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Jones, N. C., Whitfield, J. D., McMahon, P. L., Yung, M. H., Meter, R. V., Aspuru-Guzik, A., & Yamamoto, Y. (2012). Faster quantum chemistry simulation on fault-tolerant quantum computers. New Journal of Physics, 14, [115023]. https://doi.org/10.1088/1367-2630/14/11/115023