Exponentially more precise quantum simulation of fermions in second quantization

Ryan Babbush, Dominic W. Berry, Ian D. Kivlichan, Annie Y. Wei, Peter J. Love, Alán Aspuru-Guzik

Research output: Contribution to journalArticlepeer-review

90 Citations (Scopus)
34 Downloads (Pure)


We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie-Trotter-Suzuki decomposition. We present the first application of a general technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. We solve this problem with a novel quantum algorithm for on-the-fly computation of integrals that is exponentially faster than classical sampling. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most studied application of Hamiltonian simulation. Our central result is an algorithm for simulating an N spin-orbital system that requires gates. This approach is exponentially faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature.

Original languageEnglish
Article number033032
Pages (from-to)1-17
Number of pages17
JournalNew Journal of Physics
Publication statusPublished - 24 Mar 2016

Bibliographical note

Copyright the Publishers 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • electronic structure theory
  • quantum algorithms
  • quantum simulation


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