Exponentially more precise quantum simulation of fermions in second quantization

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 t...

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Bibliographic Details
Published in:New journal of physics Vol. 18; no. 3; pp. 33032 - 33048
Main Authors: Babbush, Ryan, Berry, Dominic W, Kivlichan, Ian D, Wei, Annie Y, Love, Peter J, Aspuru-Guzik, Alán
Format: Journal Article
Language:English
Published: Bristol IOP Publishing 24.03.2016
Subjects:
Algorithms
Complexity
Computation
Computer simulation
electronic structure theory
Fermions
Measurement
Organic chemistry
Physics
quantum algorithms
Quantum chemistry
quantum simulation
Taylor series
ISSN:1367-2630, 1367-2630
Online Access:Get full text
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Summary: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.
Bibliography:NJP-104092.R1
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ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/18/3/033032