Exponentially More Precise Quantum Simulation of Fermions in Second Quantization
Venue
New Journal of Physics, vol. 18 (2016), pp. 033032
Publication Year
2016
Authors
Ryan Babbush, Dominic Berry, Ian Kivlichan, Annie Wei, Peter Love, Alán Aspuru-Guzik
BibTeX
Abstract
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 O(N^5 t) 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.
