Can I install Portage, Pacman or other package managers on Ubuntu?

You don't. A package manager is central to a specific distribution. Gentoo, Arch, Redhat -- they all use different packaging systems. Gentoo's portage packages usually compile from source, Arch uses its own binary package format, Redhat uses RPM as packaging system -- and Debian as well as Ubuntu and Linux Mint use Debian Packages (.deb). Managing your local installation takes place using graphical frontends like Synaptic and Adept, or command-line tools like apt-get, aptitude and dpkg.

Though it is possible to install other package managers on Ubuntu (else they wouldn't be in the repositories), this is not to be recommended for the unexperienced user. One should be quite familiar with packages and package managers, how they work, etc. before even thinking about using them alongside. Otherwise it is very likely to end up with a very broken system -- as one package manager is not aware of the others, they would e.g. overwrite each others files/configurations, uninstalling a package with one package manager could break dependencies with the other, and more.

So for now I'd strongly suggest you stay with the package managers native to your system (see above).

You cannot should not

Package managers are usually very tightly integrated with a particular Linux distribution, and you cannot usually install a native manager for one distro onto another and expect it to just work. (but see note at the end)

You can install the resulting packages, however, using tools to convert e.g. RPM to DEB, etc. This may be possible for Pacman packages. Portage, as you may be aware, builds everything from source, and you can do this on any distro, not just Gentoo.

Note: While some like yum are available in the Ubuntu Universe repositories, and even Pacman, Portage etc. could be installed in theory, it's a bad idea in practice because the packages themselves may not be suited (directory structure, etc.) for Ubuntu.

Due to the different packaging systems, the package managers are not interchangeable without a lot of blood, sweat and tears. Even then, there are a lot of dependency issues, and bugs, and errors, and rabbit holes that you cannot find your way out of. No, it's not it's not impossible, but, it's not recommended. PacApt is your best bet to use Pacman AND Portage commands in Ubuntu without destroying your computer. I believe that it supports commands from all of the major package managers. This is probably your safest bet for installation of Pacman/Portage-likeness in Ubuntu. Check it out.

If it isn't what you are looking for, your best bet (and recommended course of action) may be to install the distribution of the package manager that you want to use.

PacApt Brings Arch Linux’s Amazing Pacman Package Manager to Other Linux Distributions (Well, Sort Of)

Source:  LifeHacker