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What are the different kinds of computation that exist? From what I can see, there are two kinds:
I am wondering if there are more kinds of computation or whether philosophers use different criteria to distinguish between different kinds of computation.
Types of computation are not based on the type of device but on the way in which information is structured and processed. The principal types are analogue, digital and quantum. (What follows is updated following comments and downvotes made).
For example an abacus is a digital (ON/OFF) computer, albeit using decimal word lengths rather than bit-count word lengths. Some early electronic computers used the same decimal system, as did Babbage's mechanical Difference Engine of the late 19th century. A box of counters, a pencil and a sheet of paper are an even simpler, though rather more flexible, digital computer. Powerful ones just happen to be electronic these days.
By contrast an analogue computer processes signals (numbers) which are continuously variable across the working range. Analogue computers have been mechanical as in the computing gunsights fitted to American bombers in WWII, electrical as in some early aircraft control systems, or even hydraulic as in the first ever computational model of the UK economy.
A quantum computer operates on a third principle again. Where a digital process is discrete and analog is continuous, a quantum process is a superposition of all possibilities. A quantum computer typically comprises a set of components called qbits, which are linked or entangled together in such a way as to collectively processes a near-infinite superposition of intangible possibilities before they find the most likely answer. Other more exotic quantum architectures also exist, which are not bound by the "bit" model necessary to communicate with a discrete-logic controller. Although the quantum processor is surrounded by a conventional digital control system, the core processor itself is anything but digital. These devices are at a very early stage of development and to say more requires a degree in advanced ... - you know, I don't even know what you do need to know.
The human or animal brain is, broadly speaking, an analogue device in terms of its chemistry but digital in the way it encodes nerve signals as pulse trains. Nobel prize-winning physicist and mathematician Roger Penrose is among those who have argued that neural processing, especially memory, also depends on quantum phenomena.
A neural network is a technological architecture which seeks to emulate certain features of human brain activity. Neural networks are commonly used for AI applications involving big data and deep learning. Typically, at some point a digital device will be used to simulate an analogue function (which is itself an approximation of the original neural digital pulse train). Theoretically an analogue device known as a memristor would greatly improve circuit efficiency, but only experimental memristor-like circuit modules have yet been developed. Working systems remain all-digital emulations.
Well, there are different kinds of physical computers as the other answer touched on. But if you're asking about types of computation, then in mathematics and computer science this often refers to formal systems that are able to calculate different classes of functions. See the article on automata theory which highlights four important models of computation, and then goes on to describe a lot more.
These are four important and common models of computation, but there are more. There are the primitive recursive functions which can calculate anything a pushdown automaton can calculate, but can't calculate as much as a Turing machine. There are hypercomputation and oracle machines which are more powerful than Turing machines, but cannot be physically implemented as far as we know. There are also many models of computation that are equivalent to some already mentioned, many of which are laid out in the article on automata theory. Some examples are lambda calculus, combinatory logic, cellular automata, non-deterministic Turing machines, Post canonical systems.
