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arXiv · 2401.07934

Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem

P. Singkanipa·V. Kasatkin·Z. Zhou·G. Quiroz·D. A. Lidar
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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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P. Singkanipa, V. Kasatkin, Z. Zhou, G. Quiroz, D. A. Lidar. 2024-01-15. Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem. https://doi.org/10.1103/physrevx.15.021082

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