Steps to reproduce:
1. Open the attached project (case_1205146-CSBug.zip)
2. Load the "DemoScene" scene (Drag it from Project/Scenes to the Hierarchy)
3. Enter Play Mode
4. Observe the value displayed in the top-left corner of the Game window and/or outputted to the console
5. In project settings under "Player" (Edit > Project Settings > Player), uncheck "Auto Graphics API for Windows" and switch the Graphics API to Vulkan
6. Unity will prompt you to restart, click "Restart Editor"
7. After restarting, enter Play Mode again

Expected results: Correct value is displayed on the screen and outputted to the console (should be 5)
Actual results: The value is either 0 or some other arbitrary number

Reproduced in: 2018.3.0a4, 2018.4.15f1, 2019.2.17f1, 2019.3.0f3, 2020.1.0a17
Not reproducible in: 2017.4.35f1, 2018.3.0a3

Note: It's possible that in 2018.3.0a3 and earlier Unity fallbacks and uses the D3D11 compiled Shader since both Vulkan and D3D11 compiled ComputeShader code is present, even when Vulkan is the only Graphics API selected.