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

TL;DR

This paper demonstrates exponential quantum speedup on current superconducting quantum processors for a version of Simon's problem by using hardware-aware compilation to achieve constant-depth circuits.

Contribution

It introduces a hardware-aware compilation strategy that enables exponential quantum speedup on NISQ devices for Simon's problem.

Findings

Achieved exponential speedup over classical lower bounds on IBM quantum processors.

Compiled circuits have constant depth and linear connectivity, suitable for current hardware.

Observed polynomial speedup at higher Hamming weights on Miami processor.

Abstract

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.