Work

Solving the Subset Sum Problem via Quantum Walk Search

Year: 2025

Type: article

Abstract: Quantum walk-based search algorithms have demonstrated an asymptotic quadratic speedup compared to classical search methods. Formulating a generic search problem as a (quantum) search over a graph makes the efficiency of the algorithm to be closely dependent on the properties of the graph itself. In this work, we present a complete implementation of a quantum walk search procedure on Johnson graphs, speeding up the solution of the Subset Sum Problem, a well-known computational problem with applications in resource allocation, scheduling, and cryptanalysis. We provide a detailed design of each sub-circuit, quantifying their costs in terms of gate count, circuit depth, and qubit width, and exhibit all figures of merit as a function of the problem parameters. Our approach includes two distinct implementations: one that minimizes qubit usage and another focused on optimizing circuit depth. We compare our solutions against the unstructured Grover based quantum search algorithm, demonstrating a reduction of the cost on terms of T-count and T-depth, for practically solvable instances. The proposed design serves as a foundational building block for the development of efficient quantum search algorithms that can be modeled on Johnson graphs, bridging the gap with existing theoretical complexity analyses.

Source: IEEE Transactions on Computers

DOI: 10.1109/tc.2025.3625044

Authors: Giacomo Lancellotti, Simone Perriello, Alessandro Barenghi, Gerardo Pelosi

Institution: Politecnico di Milano

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,645

Funder: Ministero dell'Università e della Ricerca