Qrisp-Based Implementation and Experimental Evaluation of a T-Count-Optimized Non-Restoring Quantum Square-Root Circuit

Efficient quantum arithmetic is a prerequisite for the practical realization of large-scale quantum algorithms, yet many resource-optimized designs remain at the theoretical level. In this work, we present a complete implementation of the T-count-optimized non-restoring quantum square-root circuit proposed by Muñoz-Coreas E. and Thapliyal H. in the Qrisp quantum programming framework. The implemented design follows the garbageless square-root construction based on reversible arithmetic and is built from modular sub-circuits, including reversible adders, subtractors, controlled add/subtract blocks, and controlled adders. We show that the high-level abstractions provided by Qrisp enable a direct and reusable realization of the algorithm while preserving the theoretical resource advantages of the original circuit. To assess practical feasibility, the circuits were additionally executed on IBM’s ibmₘarrakesh superconducting quantum processor. The experimental results show that the algorithm can run on contemporary NISQ hardware for small input sizes, although compilation overhead, two-qubit gate errors, readout errors, and relaxation effects significantly reduce success rates as the circuit size increases. Among the tested runtime techniques, dynamical decoupling provided only limited improvement. These results establish the practical realizability of a resource-efficient quantum square-root circuit and provide insight into the challenges of executing arithmetic-heavy quantum algorithms on present-day hardware. These results demonstrate that the previously proposed T-count-optimized non-restoring square-root circuit can be realized as a modular Qrisp implementation, exported to Qiskit, and experimentally evaluated on contemporary NISQ hardware, while also highlighting the practical limitations imposed by compilation overhead and hardware noise.