The fundamental unit of quantum computation is the “qubit”, the quantum analogue of the ordinary “bit” in a standard machine. Like ordinary bits, qubits can take the value of 1 or 0. Unlike ordinary bits, their quantum nature also lets them exist in a strange mixture—a “superposition”, in the jargon—of both states at once, much like Erwin Schrödinger’s famous cat. That means that a quantum computer can be in many states simultaneously, which in turn means that it can, in some sense, perform many different calculations at the same time. To be precise, a quantum computer with four qubits could be in 2^4 (ie, 16) different states at a time. As you add qubits, the number of possible states rises exponentially. A 16-bit quantum machine can be in 2^16, or 65,536, states at once, while a 128-qubit device could occupy 3.4 x 10^38 different configurations, a colossal number which, if written out in longhand, would have 39 digits. Having been put into a delicate quantum state, a quantum computer can thus examine billions of possible answers simultaneously.
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We should probably note that while D-Wave systems are not really quantum computers in the classical sense, they do use quantum effects. How do they do it? Check out this paper on Quantum Annealing with More than One Hundred Qubits.