Chemical reactions are regarded as transformations of chemical structures, and the question of which atoms in the reactants correspond to which atoms in the products has attracted chemists for a long time. Atom-to-atom mapping (AAM) is a procedure that establishes such correspondence(s) between the atoms of reactants and products in a chemical reaction. Currently, automatic AAM tools play a pivotal role in various chemoinformatics tasks. However, achieving accurate automatic AAM for complex or unknown reactions within a reasonable computation time remains a significant challenge due to the combinatorial nature of the problem and the difficulty in applying appropriate reaction rules. In this study, we propose a rule-free AAM algorithm, which enumerates all atom-to-atom correspondences that minimize the number of bond cleavages and formations during the reaction. To reduce the computational burden associated with the combinatorial optimization (i.e., minimizing bond changes), we introduce Ising computing, a computing paradigm that has gained significant attention for its efficiency in solving hard combinatorial optimization problems. We found that our Ising computing framework outperforms conventional combinatorial optimization algorithms in terms of computation times, making it feasible to solve the AAM problem without reaction rules in an acceptable time. Furthermore, our AAM algorithm successfully found the correct AAM solution for all problems in a benchmark data set. In contrast, conventional AAM algorithms based on chemical heuristics failed for several problems. Specifically, these algorithms either failed to find the optimal solution in terms of bond changes, or they identified only one optimal solution, which was incorrect when multiple optimal solutions exist. These results emphasize the importance of enumerating all optimal correspondences that minimize bond changes, which is effectively achieved by our Ising-computing framework.