Optimising Matrix Product State Simulations of Shor's Algorithm
We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2019-01-25-116/pdf/ |
| _version_ | 1818289584205725696 |
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| author | Aidan Dang Charles D. Hill Lloyd C. L. Hollenberg |
| author_facet | Aidan Dang Charles D. Hill Lloyd C. L. Hollenberg |
| author_sort | Aidan Dang |
| collection | DOAJ |
| description | We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping. |
| first_indexed | 2024-12-13T02:14:36Z |
| format | Article |
| id | doaj.art-77dfbbd220504ffcae5c35ad938ddb29 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-13T02:14:36Z |
| publishDate | 2019-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-77dfbbd220504ffcae5c35ad938ddb292022-12-22T00:02:55ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-01-01311610.22331/q-2019-01-25-11610.22331/q-2019-01-25-116Optimising Matrix Product State Simulations of Shor's AlgorithmAidan DangCharles D. HillLloyd C. L. HollenbergWe detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.https://quantum-journal.org/papers/q-2019-01-25-116/pdf/ |
| spellingShingle | Aidan Dang Charles D. Hill Lloyd C. L. Hollenberg Optimising Matrix Product State Simulations of Shor's Algorithm Quantum |
| title | Optimising Matrix Product State Simulations of Shor's Algorithm |
| title_full | Optimising Matrix Product State Simulations of Shor's Algorithm |
| title_fullStr | Optimising Matrix Product State Simulations of Shor's Algorithm |
| title_full_unstemmed | Optimising Matrix Product State Simulations of Shor's Algorithm |
| title_short | Optimising Matrix Product State Simulations of Shor's Algorithm |
| title_sort | optimising matrix product state simulations of shor s algorithm |
| url | https://quantum-journal.org/papers/q-2019-01-25-116/pdf/ |
| work_keys_str_mv | AT aidandang optimisingmatrixproductstatesimulationsofshorsalgorithm AT charlesdhill optimisingmatrixproductstatesimulationsofshorsalgorithm AT lloydclhollenberg optimisingmatrixproductstatesimulationsofshorsalgorithm |