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While Vision Transformers (ViTs) have shown consistent progress in computer vision, deploying them for real-time decision-making scenarios (< 1 ms) is challenging. Current computing platforms like CPUs, GPUs, or FPGA-based solutions struggle to meet this deterministic low-latency real-time requirement, even with quantized ViT models. Some approaches use pruning or sparsity to reduce model size and latency, but this often results in accuracy loss. To address the aforementioned constraints, in this work, we propose EQ-ViT, an end-to-end acceleration framework with novel algorithm and architecture co-design features to enable real-time ViT acceleration on AMD Versal Adaptive Compute Acceleration Platform (ACAP). The contributions are four-fold. First, we perform in-depth kernel- level performance profiling & analysis and explain the bottlenecks for existing acceleration solutions on GPU, FPGA, and ACAP. Second, on the hardware level, we introduce a new spatial and heterogeneous accelerator architecture, EQ-ViT architec- ture. This architecture leverages the heterogeneous features of ACAP, where both FPGA and artificial intelligence engines (AIEs) coexist on the same system-on-chip (SoC). Third, On the algorithm level, we create a comprehensive quantization-aware training strategy, EQ-ViT algorithm. This strategy concurrently quantizes both weights and activations into 8-bit integers, aiming to improve accuracy rather than compromise it during quanti- zation. Notably, the method also quantizes nonlinear functions for efficient hardware implementation. Fourth, we design EQ- ViT automation framework to implement the EQ-ViT architec- ture for four different ViT applications on the AMD Versal ACAP VCK190 board, achieving accuracy improvement with 2.4%, and average speedups of 315.0x, 3.39x, 3.38x, 14.92x, 59.5x, 13.1x over computing solutions of Intel Xeon 8375C vCPU, Nvidia A10G, A100, Jetson AGX Orin GPUs, and AMD ZCU102, U250 FPGAs. The energy efficiency gains are 62.2x, 15.33x, 12.82x, 13.31x, 13.5x, 21.9x.