A quantum computer is a hypothetical machine that would exploit the principles of quantum mechanics that govern the subatomic world, in order to solve certain problems much faster than we know how to solve them with any computer today. Quantum mechanics has been the basic framework for almost all of physics for nearly a century. What is says is that if you don’t know what state a system is in – like you don’t know if an electron is in its ground state, its lowest energy or in the next higher energy – well the issue is in quantum mechanics the different places where the particle could be, or the different paths that it could take to reach a certain final position can all interfere with each other. And if that happens then these different paths can cancel each other out. So then if some are positive and others are negative then maybe you won’t find the particle at that final place at all. A classical computer, you know, is of course based on bits which are a bunch of elements that can be either definitely zero or definitely one. Now a quantum computer is based on a quantum bit, or q-bits, which can be, as we say, in a quantum super position of the zero and one states. Now the way most popular articles like to put it is that it can be zero and one at the same time. And the problem is that at some point you’ve got to measure the computer to figure out or to read out an answer. Which answer you see is determined by these amplitudes. An amplitude is like the square root of a probability. Now the key point is that the same number can have more than one square root. For example, “2” and “-2” are both square roots of “4”. So corresponding to that you can have either a positive or a negative amplitude. So now, what a quantum computer would be is a computer that would exploit this phenomenon of interference between positive and negative amplitudes on a massive scale. And the goal would be that you would try to, sort of, choreograph things so that all of the different paths leading to a wrong answer would be out of phase. Some would have positive amplitudes. Others would have negative amplitudes. And so they would cancel each other out. Whereas the paths leading to a right answer should all have the same sign. They should all reinforce each other. And if you can arrange that, then when you look at the computer, at the end, then you’re going to see the right answer with high probability. Probably the most dramatic application of a quantum computer, the one that makes the headlines, is that it could break almost all of the cryptography that we use today to protect our credit card numbers. But that’s actually, probably not the most useful application. Maybe its useful if you’re the first to do it and you don’t tell anyone else about it, but it will mean that the world will have to switch to other cryptographic codes when this starts to become practical. Maybe a much more useful application is one thats actually the first one that the physicists thought of back in the 1980s. And one that is so obvious that we barely even talk about it. Namely you can use a quantum computer to simulate quantum physics. For example if you are designing pharmaceuticals. Or, if you’re trying to design new nano materials. If you’re trying to understand high-tempurature superconductors or do high-energy physics. Or do quantum chemistry. For any of these applications, any place where we’re sort of understanding the quantum behavior of atoms and molecules is relevant, well a quantum computer sort of naturally implements those dynamics and so it could give you huge speed- ups in simulating those sorts of things. And, probably the third application of quantum computers is that you can try and throw them at these np complete problems. Like, combinatorial optimization problems like airline scheduling. Or like the traveling salesmen problem. Any problem where you have a whole bunch of constraints that you’re trying to satisfy. This is a huge, huge class of practical problems that people try to solve. But now for these problems we don’t yet know, sort of, how much an advantage quantum computers are actually going to give you. If there’s some fundamental reason why you can’t build a quantum computer then I hope that we discover that because that would be a hundred times more exciting than success in building one. In principle impossibility of quantum computers would force us to revise our whole conception of the laws of physics.