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The neural network enables efficient solutions for Nondeterministic Polynomial-time (NP) hard problems, which are challenging for conventional von Neumann computing. The hardware implementation, i.e., neuromorphic computing, aspires to enhance this efficiency by custom hardware. Particularly, NP hard graphical constraint optimization problems are solved by a network of stochastic binary neurons to form a Boltzmann Machine (BM). The implementation of stochastic neurons in hardware is a major challenge. In this work, we demonstrate that the high to low resistance switching (set) process of a PrxCa1−xMnO3 (PCMO) based RRAM (Resistive Random Access Memory) is probabilistic. Additionally, the voltage-dependent probability distribution approximates a sigmoid function with 1.35%–3.5% error. Such a sigmoid function is required for a BM. Thus, the Analog Approximate Sigmoid (AAS) stochastic neuron is proposed to solve the maximum cut—an NP hard problem. It is compared with Digital Precision-controlled Sigmoid (DPS) implementation using (a) pure CMOS design and (b) hybrid (RRAM integrated with CMOS). The AAS design solves the problem with 98% accuracy, which is comparable with the DPS design but with 10× area and 4× energy advantage. Thus, ASIC neuro-processors based on novel analog neuromorphic devices based BM are promising for efficiently solving large scale NP hard optimization problems.