Smart refrigerators sure are convenient. They include special-purpose computers that can create shopping lists for you. Your laptop probably doesn’t do that by default, but your laptop does a plethora of other things. You can design a web page, write a paper, program a cat qubit quantum computer, and you can even create a shopping list the old-fashioned way. In a similar context, we can differentiate special-purpose quantum computers from universal quantum computers.
Special-purpose quantum computers are the quantum analogues of Application-Specific Integrated Circuits (ASIC). They execute a subset of quantum algorithms with the expectation that they can solve such algorithms particularly well. Quantum annealers and analog quantum computers are prominent examples. Their limitations are by design, sacrificing any intentions of doing everything, simplifying qubit control, and focusing on performing specific tasks. There is considerable exploration into where such devices might offer computational advantages.
Universal quantum computers, in contrast, can do it all. They control and execute operations on each qubit individually. Consequently, they can execute any gate-based quantum algorithm, including algorithms for the same types of problems that you might use special-purpose quantum computers. Importantly, the quantum algorithms with known speed-ups over classical algorithms – Shor’s and Grover’s, for example – run exclusively on universal quantum computers.
With simpler controls, a special-purpose device usually has more qubits and can generally tackle larger problems. With complex controls, a universal device can still solve those problems, but it can also solve all the other problems. Ironically, special-purpose devices can solve larger problems, but universal devices can solve the biggest problems.