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...

Full description

Saved in:
Bibliographic Details
Main Authors: Phattharaporn Singkanipa, Victor Kasatkin, Zeyuan Zhou, Gregory Quiroz, Daniel A. Lidar
Format: Article
Language:English
Published: American Physical Society 2025-06-01
Series:Physical Review X
Online Access:http://doi.org/10.1103/PhysRevX.15.021082
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849434424046780416
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
work_keys_str_mv AT phattharapornsingkanipa demonstrationofalgorithmicquantumspeedupforanabelianhiddensubgroupproblem
AT victorkasatkin demonstrationofalgorithmicquantumspeedupforanabelianhiddensubgroupproblem
AT zeyuanzhou demonstrationofalgorithmicquantumspeedupforanabelianhiddensubgroupproblem
AT gregoryquiroz demonstrationofalgorithmicquantumspeedupforanabelianhiddensubgroupproblem
AT danielalidar demonstrationofalgorithmicquantumspeedupforanabelianhiddensubgroupproblem