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Paper 1

Demonstration of Exponential Quantum Speedup with Constant-Depth Compiled Circuits for Simon's Problem

Phattharaporn Singkanipa, Victor Kasatkin, Daniel A. Lidar

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.27457

arXiv

2604.27457

We demonstrate exponential quantum speedup for a restricted-Hamming-weight version of Simon's problem on present-day superconducting quantum processors by introducing a hardware-aware compilation strategy that compiles the quantum part of each Simon query circuit to constant depth. The resulting compiled circuits have $O(1)$ depth and linear connectivity, map directly onto common device layouts, and avoid additional routing and SWAP overhead. Implemented on IBM's $156$-qubit Boston and $120$-qubit Miami processors, the resulting circuits achieve sufficiently high fidelity to exhibit algorithmic quantum speedup without error suppression. Using the number-of-queries-to-solution metric, we observe exponential speedup over the classical lower bound across the full Hamming-weight range studied on Boston and across low-to-intermediate Hamming weights on Miami; at higher Hamming weights on Miami, we still observe polynomial speedup. The same construction also reaches a regime where the original Simon problem is recovered for the problem sizes studied. These results show that careful hardware-aware compilation can make exponential quantum speedup experimentally accessible for a canonical hidden-subgroup problem in the NISQ regime.

Paper 2

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