QUEST is a programmable multiple instruction, multiple data (MIMD) parallel accelerator for general-purpose state-of-the-art deep neural networks (DNNs). It features die-to-die stacking with three-cycle latency, 28.8 GB/s, 96 MB, and eight SRAMs using an inductive coupling technology called the ThruChip interface (TCI). By stacking the SRAMs instead of DRAMs, lower memory access latency and simpler hardware are expected. This facilitates in balancing the memory capacity, latency, and bandwidth, all of which are in demand by cutting-edge DNNs at a high level. QUEST also introduces log-quantized programmable bit-precision processing for achieving faster (larger) DNN computation (size) in a 3-D module. It can sustain higher recognition accuracy at a lower bitwidth region compared to linear quantization. The prototype QUEST chip is integrated in the 40-nm CMOS technology, and it achieves 7.49 tera operations per second (TOPS) peak performance in binary precision, and 1.96 TOPS in 4-bit precision at 300-MHz clock.