Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem
Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-06-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.15.021082 |
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| _version_ | 1849434424046780416 |
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| author | Phattharaporn Singkanipa Victor Kasatkin Zeyuan Zhou Gregory Quiroz Daniel A. Lidar |
| author_facet | Phattharaporn Singkanipa Victor Kasatkin Zeyuan Zhou Gregory Quiroz Daniel A. Lidar |
| author_sort | Phattharaporn Singkanipa |
| collection | DOAJ |
| description | Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight w. For sufficiently small values of w and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of w values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem. |
| format | Article |
| id | doaj-art-8d8c82be7dde42cb883fdd34f79e6d5f |
| institution | Kabale University |
| issn | 2160-3308 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-8d8c82be7dde42cb883fdd34f79e6d5f2025-08-20T03:26:39ZengAmerican Physical SocietyPhysical Review X2160-33082025-06-0115202108210.1103/PhysRevX.15.021082Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup ProblemPhattharaporn SingkanipaVictor KasatkinZeyuan ZhouGregory QuirozDaniel A. LidarSimon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight w. For sufficiently small values of w and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of w values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.http://doi.org/10.1103/PhysRevX.15.021082 |
| spellingShingle | Phattharaporn Singkanipa Victor Kasatkin Zeyuan Zhou Gregory Quiroz Daniel A. Lidar Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem Physical Review X |
| title | Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem |
| title_full | Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem |
| title_fullStr | Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem |
| title_full_unstemmed | Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem |
| title_short | Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem |
| title_sort | demonstration of algorithmic quantum speedup for an abelian hidden subgroup problem |
| url | http://doi.org/10.1103/PhysRevX.15.021082 |
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