Logic Gates Circuit -to- VHDL -to- IC ??

Hi everyone i hope you are all doing well 
im a schematic Entry designer. i design, create and draw logic gates/Flip Flops circuits using NI Multism PLD desinger, and then export that design into a VHDL file and synthesize in a FPGA IDE for real FPGA simulation.

- This an example of a digital button de-bouncer

Now i after i confirmed that circuit is working i want to create an actual IC out of it (or ASIC) but before manufacturing and chosign the fabricator, i have to create the transistor-level layout or photo mask (i actually don't know what  that file called) and i heard that Cadence can do that but :
- Does Cadence support pure digital logic design, and which version of Cadence do i need?
- Do i have to start from scratch (rebuild it all manually) or just convert my VHDL file into that "transistor-level layout design"
any suggestions or information will be appreciated 

Thank you for your time