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Neural implicit representations have shown remarkable abilities in jointly modeling geometry, color, and camera poses in simultaneous localization and mapping (SLAM). Current methods use coordinates, positional encodings, or other geometry features as input to query neural implicits for signed distances and color which produce rendering errors to drive the optimization in overfitting image observations. However, due to the run time efficiency requirement in SLAM, we are merely allowed to conduct optimization on each frame in few iterations, which is far from enough for neural networks to overfit these queries. The underfitting usually results in severe drifts in camera tracking and artifacts in reconstruction. To resolve this issue, we propose query quantized neural SLAM which uses quantized queries to reduce variations of input for much easier and faster overfitting a frame. To this end, we quantize a query into a discrete representation with a set of codes, only allow neural networks to observe a finite number of variations. This makes neural networks get more and more familiar to these codes after overfitting more and more previous frames. Moreover, we also introduce novel initialization, losses, and argumentation to stabilize the optimization with huge uncertainty in the early optimization, constrain the optimization space, and estimate camera poses more accurately. We justify the effectiveness of each design and report visual and numerical comparisons on widely used benchmarks to show our superiority over the latest methods in both reconstruction and camera tracking.