Tailoring term truncations for electronic structure calculations using a linear combination of unitaries
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we p...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022
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| _version_ | 1826307646852956160 |
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| author | Meister, R Benjamin, SC Campbell, ET |
| author_facet | Meister, R Benjamin, SC Campbell, ET |
| author_sort | Meister, R |
| collection | OXFORD |
| description | A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth. |
| first_indexed | 2024-03-07T07:07:50Z |
| format | Journal article |
| id | oxford-uuid:7ceedf85-dcec-4609-a719-6d4ba638f20a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:07:50Z |
| publishDate | 2022 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | dspace |
| spelling | oxford-uuid:7ceedf85-dcec-4609-a719-6d4ba638f20a2022-05-16T12:19:13ZTailoring term truncations for electronic structure calculations using a linear combination of unitariesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7ceedf85-dcec-4609-a719-6d4ba638f20aEnglishSymplectic ElementsVerein zur Förderung des Open Access Publizierens in den Quantenwissenschaften2022Meister, RBenjamin, SCCampbell, ETA highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth. |
| spellingShingle | Meister, R Benjamin, SC Campbell, ET Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title | Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title_full | Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title_fullStr | Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title_full_unstemmed | Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title_short | Tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
| title_sort | tailoring term truncations for electronic structure calculations using a linear combination of unitaries |
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