Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem

• URL: http://arxiv.org/abs/2401.07934v3
• Date: Sun, 12 Jan 2025 15:42:52 GMT
• Title: Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem
• Authors: P. Singkanipa, V. Kasatkin, Z. Zhou, G. Quiroz, D. A. Lidar,
• Abstract summary: Simon's problem is to find a hidden period encoded into an unknown 2-to-1 function.<n>We demonstrate an algorithmic quantum speedup for a variant of Simon's problem where the hidden period has a restricted Hamming weight $w$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

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