Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors
Abstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configu...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2021-08-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-021-95973-w |
| _version_ | 1797864638814093312 |
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| author | Unathi Skosana Mark Tame |
| author_facet | Unathi Skosana Mark Tame |
| author_sort | Unathi Skosana |
| collection | DOAJ |
| description | Abstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits. |
| first_indexed | 2024-04-09T22:55:07Z |
| format | Article |
| id | doaj.art-83ad215236954f3fa443398042bc8bfa |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-09T22:55:07Z |
| publishDate | 2021-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-83ad215236954f3fa443398042bc8bfa2023-03-22T11:19:05ZengNature PortfolioScientific Reports2045-23222021-08-0111111210.1038/s41598-021-95973-wDemonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processorsUnathi Skosana0Mark Tame1Department of Physics, Stellenbosch UniversityDepartment of Physics, Stellenbosch UniversityAbstract We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.https://doi.org/10.1038/s41598-021-95973-w |
| spellingShingle | Unathi Skosana Mark Tame Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors Scientific Reports |
| title | Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors |
| title_full | Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors |
| title_fullStr | Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors |
| title_full_unstemmed | Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors |
| title_short | Demonstration of Shor’s factoring algorithm for N $$=$$ = 21 on IBM quantum processors |
| title_sort | demonstration of shor s factoring algorithm for n 21 on ibm quantum processors |
| url | https://doi.org/10.1038/s41598-021-95973-w |
| work_keys_str_mv | AT unathiskosana demonstrationofshorsfactoringalgorithmforn21onibmquantumprocessors AT marktame demonstrationofshorsfactoringalgorithmforn21onibmquantumprocessors |