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...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/18/3/033032 |
| _version_ | 1797751028547846144 |
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| author | Ryan Babbush Dominic W Berry Ian D Kivlichan Annie Y Wei Peter J Love Alán Aspuru-Guzik |
| author_facet | Ryan Babbush Dominic W Berry Ian D Kivlichan Annie Y Wei Peter J Love Alán Aspuru-Guzik |
| author_sort | Ryan Babbush |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:41:25Z |
| format | Article |
| id | doaj.art-5e585ff64a4c42a9b71d17faf5934fd7 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:41:25Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5e585ff64a4c42a9b71d17faf5934fd72023-08-08T14:28:04ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118303303210.1088/1367-2630/18/3/033032Exponentially more precise quantum simulation of fermions in second quantizationRyan Babbush0Dominic W Berry1Ian D Kivlichan2Annie Y Wei3Peter J Love4Alán Aspuru-Guzik5Department of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USA; Google, Venice, CA 90291, USADepartment of Physics and Astronomy, Macquarie University , Sydney, NSW 2109, AustraliaDepartment of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USA; Department of Physics, Harvard University , Cambridge, MA 02138, USADepartment of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USADepartment of Physics and Astronomy, Tufts University , Medford, MA 02155, USADepartment of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USAWe 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.https://doi.org/10.1088/1367-2630/18/3/033032quantum algorithmsquantum simulationelectronic structure theory |
| spellingShingle | Ryan Babbush Dominic W Berry Ian D Kivlichan Annie Y Wei Peter J Love Alán Aspuru-Guzik Exponentially more precise quantum simulation of fermions in second quantization New Journal of Physics quantum algorithms quantum simulation electronic structure theory |
| title | Exponentially more precise quantum simulation of fermions in second quantization |
| title_full | Exponentially more precise quantum simulation of fermions in second quantization |
| title_fullStr | Exponentially more precise quantum simulation of fermions in second quantization |
| title_full_unstemmed | Exponentially more precise quantum simulation of fermions in second quantization |
| title_short | Exponentially more precise quantum simulation of fermions in second quantization |
| title_sort | exponentially more precise quantum simulation of fermions in second quantization |
| topic | quantum algorithms quantum simulation electronic structure theory |
| url | https://doi.org/10.1088/1367-2630/18/3/033032 |
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