Identifying the physical locations of neurons based on the spike waveforms captured by multiple recording channels, namely spike localization, can potentially enhance spike sorting accuracy. This study proposes a new method for spike localization, where the problem is first described as a nonconvex optimization problem and then the optimization is attempted heuristically via a numerical Ising solver. The paper first presents a quadratic unconstrained binary optimization (QUBO) formulation of spike localization. Then, a MATLAB solver simulating an Ising machine is written to solve the QUBO. The proposed method is evaluated on a 2D toy problem consisting of two electrodes and a single spike event, where the neuron location search is conducted in three different regions placed at increasing distances from the electrodes. The results indicate that the neuron can be accurately identified when in one of the nearest nodes to the electrodes, whereas the accuracy decreases to 87.5% and 75% as the search region distance increases. The study for the first time formulates the spike localization problem as a QUBO and demonstrates the feasibility of solving the resultant non-convex optimization problem heuristically using an Ising machine.Clinical Relevance- High channel-count implantable neural monitoring systems allow tracking large brain regions at the cost of increased data volumes to transmit and power dissipation. The new spike localization approach presented can potentially decrease the data volume and power consumption by enabling high accuracy spike localization at the implantable system.