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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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
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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 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.
AbstractList	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 $\tilde{{ \mathcal O }}({N}^{5}t)$ 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. 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.
Author	Kivlichan, Ian D Wei, Annie Y Babbush, Ryan Aspuru-Guzik, Alán Berry, Dominic W Love, Peter J
Author_xml	– sequence: 1 givenname: Ryan surname: Babbush fullname: Babbush, Ryan email: ryanbabbush@gmail.com organization: Google, Venice, CA 90291, USA – sequence: 2 givenname: Dominic W surname: Berry fullname: Berry, Dominic W email: dominic.berry@mq.edu.au organization: Macquarie University Department of Physics and Astronomy, Sydney, NSW 2109, Australia – sequence: 3 givenname: Ian D surname: Kivlichan fullname: Kivlichan, Ian D organization: Harvard University Department of Physics, Cambridge, MA 02138, USA – sequence: 4 givenname: Annie Y surname: Wei fullname: Wei, Annie Y organization: Harvard University Department of Chemistry and Chemical Biology, Cambridge, MA 02138, USA – sequence: 5 givenname: Peter J surname: Love fullname: Love, Peter J organization: Tufts University Department of Physics and Astronomy, Medford, MA 02155, USA – sequence: 6 givenname: Alán surname: Aspuru-Guzik fullname: Aspuru-Guzik, Alán email: aspuru@chemistry.harvard.edu organization: Harvard University Department of Chemistry and Chemical Biology, Cambridge, MA 02138, USA
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Snippet	We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie-Trotter-Suzuki... We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie–Trotter–Suzuki...
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SubjectTerms	Algorithms Complexity Computation Computer simulation electronic structure theory Fermions Measurement Organic chemistry Physics quantum algorithms Quantum chemistry quantum simulation Taylor series
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Title	Exponentially more precise quantum simulation of fermions in second quantization
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