There is a constant need for high-performing and computationally efficient neural network models for image super-resolution (SR) often used on low-capacity devices. One way to obtain such models is to compress existing architectures, e.g. quantization. Another option is a neural architecture search (NAS) that discovers new efficient solutions. We propose a novel quantization-aware NAS procedure for a specifically designed SR search space. Our approach performs NAS to find quantization-friendly SR models. The search relies on adding quantization noise to parameters and activations instead of quantizing parameters directly. Our QuantNAS finds architectures with better PSNR/BitOps trade-off than uniform or mixed precision quantization of fixed architectures. Additionally, our search against noise procedure is up to 30% faster than directly quantizing weights.