In this study, we demonstrate a high-performance solid polymer electrolyte (SPE) atomic switching device with low SET/RESET voltages (0.25 and -0.5 V, respectively), high on/off-current ratio (10), excellent cyclic endurance (>10), and long retention time (>10 s), where poly-4-vinylphenol (PVP)/poly(melamine-co-formaldehyde) (PMF) is used as an SPE layer. To accomplish these excellent device performance parameters, we reduce the off-current level of the PVP/PMF atomic switching device by improving the electrical insulating property of the PVP/PMF electrolyte through adjustment of the number of cross-linked chains. We then apply a titanium buffer layer to the PVP/PMF switching device for further improvement of bipolar switching behavior and device stability. In addition, we first implement SPE atomic switch-based logic AND and OR circuits with low operating voltages below 2 V by integrating 5 × 5 arrays of PVP/PMF switching devices on the flexible substrate. In particular, this low operating voltage of our logic circuits was much lower than that (>5 V) of the circuits configured by polymer resistive random access memory. This research successfully presents the feasibility of PVP/PMF atomic switches for flexible integrated circuits for next-generation electronic applications.