It's just multi-state computing, like using a trinary or larger base. Currently our computers work with little pseudo-switches that are either on or off, 0 or 1.
Using multi-state switches you can exponentially increase computing power BUT... it just means a faster computer. It's not like it's going to magically turn into some kind of AI singularity due to inherent mathematical limitations, namely the "curse of dimensionality".
Also keep in mind our computers, even quantum computers, currently use a flow of electrons... which means they use mono-dimensional energy. It's possible though to use other energy forms, even biochemical energy forms as well as modulated energy forms, like light wavelengths in order to create photonic processors.
And then of course, if you want to go full science fiction you could theoretically create a quantum temporal processor using tachyons. Where a calculation could be performed and then the results of the calculation could be sent back in time by a few nanoseconds. So basically the computer would know the results of a calculation before it even performed it. And the further back in time the weirder it would get. For example if information could be sent back in time by a few seconds it would be possible to create a computer that would know what you want before you even knew you wanted it.
Essentially an interface-less computer. The interface would be there, but you wouldn't actually need to use it.