When is CUDA gonna be released for Ubuntu 20.04?

For Cuda only, you can refer to @meetnick's answer.

As per June, 16th, 2020, I managed to install CUDA 10.1 and cuDNN 7.6.5 on Ubuntu 20.04 and they work perfectly with Tensorflow 2.2.0
Here are the steps that I followed

1- Install CUDA (10.1):

As per now, there is no deb file or run file for Ubuntu 20.04, so the only solution is to run:

sudo apt install nvidia-cuda-toolkit

It will take a while to be installed.
After that, to make sure that CUDA is installed, run:

nvcc -V  

You would get an output similar to the following:

nvcc: NVIDIA (R) Cuda compiler driver
Copyright (c) 2005-2019 NVIDIA Corporation
Built on Sun_Jul_28_19:07:16_PDT_2019
Cuda compilation tools, release 10.1, V10.1.243  

This means that CUDA is successfully installed on your Ubuntu 20.04.
The slight difference is that cuda is not installed in the usual path (/usr/local/cuda, /usr/local/cuda-10.1). Instead, it is installed in /usr/lib/ (/usr/lib/cuda/).
You can get where CUDA is installed by running the following command:

whereis cuda 

2- Install cuDNN (7.6.5):

first go to this link then choose Download cuDNN. You'll be asked to login/create an account. After logging in, you'll be asked to accept the Terms of the cuDNN Software License Agreement.
A list of downloadable cuDNN will be displayed, click on Download cuDNN v7.6.5 (November 5th, 2019), for CUDA 10.1 then choose cuDNN Library for Linux.
After the download is finished, extract the file, then open the terminal and run:

cd cudnn-10.1-linux-x64-v7.6.5.32 # or whatever folder you got after extracting the file

Then:

sudo cp cuda/include/cudnn.h /usr/lib/cuda/include/

After that:

sudo cp cuda/lib64/libcudnn* /usr/lib/cuda/lib64/

Finally:

sudo chmod a+r /usr/lib/cuda/include/cudnn.h /usr/lib/cuda/lib64/libcudnn*

Once you finish, you have to add the CUDA path to your ~/.bashrc file. You need to run:

echo 'export LD_LIBRARY_PATH=/usr/lib/cuda/lib64:$LD_LIBRARY_PATH' >> ~/.bashrc
echo 'export LD_LIBRARY_PATH=/usr/lib/cuda/include:$LD_LIBRARY_PATH' >> ~/.bashrc  

Then run:

source ~/.bashrc 

3- Optional:
Now you can install Tensorflow-gpu (2.2.0) and test if uses your GPU or not.
pip3 install tensorflow-gpu==2.2.0
Then run python3 and type the following lines:

import tensorflow as tf
tf.config.list_physical_devices('GPU')

If everything went as planned, you'll get an output telling that Tensorflow has access to your GPU.


Ubuntu 20.04 LTS and CUDA 11.1 setup:

wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/cuda-ubuntu2004.pin
sudo mv cuda-ubuntu2004.pin /etc/apt/preferences.d/cuda-repository-pin-600
sudo apt-key adv --fetch-keys https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/7fa2af80.pub
sudo add-apt-repository "deb https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/ /"
sudo apt update
sudo apt install -y nvidia-kernel-source-455
sudo apt install -y nvidia-dkms-455
sudo apt install -y nvidia-driver-455
sudo apt install -y cuda-drivers-455
sudo apt install -y cuda-runtime-11-1
sudo apt install -y cuda-11-1
echo 'export PATH=/usr/local/cuda-11.1/bin${PATH:+:${PATH}}' >> $HOME/.bashrc

NVIDIA Cuda 11 Toolkit for Ubuntu 20.04 is finally released.

wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2004/x86_64/cuda-ubuntu2004.pin
sudo mv cuda-ubuntu2004.pin /etc/apt/preferences.d/cuda-repository-pin-600
wget http://developer.download.nvidia.com/compute/cuda/11.0.2/local_installers/cuda-repo-ubuntu2004-11-0-local_11.0.2-450.51.05-1_amd64.deb
sudo apt install ./cuda-repo-ubuntu2004-11-0-local_11.0.2-450.51.05-1_amd64.deb
sudo apt-key add /var/cuda-repo-ubuntu2004-11-0-local/7fa2af80.pub
sudo apt-get update
sudo apt-get -y install cuda