![]() We just have to make up the mathematical rules that we can use to calculate it.įor the two states up and down, there are only four possible overlaps to calculate and we know what they should be already. Now we have a new mathematical thing to calculate. For states that are 100% the same, let’s say that the overlap is 1. The states up and down are completely different, so these should have an overlap of 0 (this is the actual number zero this time). For quantum mechanics we’ll need some new maths, so let’s start making it up.įirstly, it would be useful to have some way of quantifying how similar two states are. But these are just sets of rules that turned out to be useful for something. This might come as a surprise to you, since you’ve probably been taught it as a set of rigid rules and methods that must be obeyed. One thing you need to know about maths is that it’s perfectly fine to make the rules up as you go along. Now let’s try to describe quantum states with maths. This will all let us avoid the weirdness of | and ⟩. Let’s also put up and down in bold to mark them out as special. For the state usually known as 1, let’s call it down. For the qubit state usually known as 0, let’s instead call it up. Instead let’s use different labels for the qubit states. This notation has scared many an undergraduate physics student, so let’s avoid it here. They are just to remind us that the 0 and 1 are names for quantum states and not actual numbers. Here the | and ⟩ aren’t going to actual do anything in any equations. To avoid this confusion, we usually write them down in a slightly strange way. So it can be confusing when we start putting them into equations. They are not really the actual numbers ‘0’ and ‘1’, that we can add and multiply. They could equally be called ‘Yes’ and ‘No’, or ‘Grey’ and ‘Pineapple’, or ‘£’ and ‘%’. Though the two basic states for a qubit are called 0 and 1, these are just labels we have chosen. We are limited to simply asking whether it is in one state (like 0) or a completely different state (like 1), and putting up with randomness in the result when it is neither. Unfortunately, there is no way to do this. It would be nice to find out exactly which of the infinite number of superposition states it is in. It would be nice to get more information out of a qubit. If the superposition is more biased towards 0, you’ll most likely get 0 and vice-versa. If its state is not 0 or 1, but is instead in a superposition of them, the qubit will randomly choose which one to be. You can also ask the same question of qubits. When you measure a bit, you ask it whether it is in state 0 or state 1. But it can also be one of an infinite number of superposition states, where it is some degree of 0 and some degree of 1 at the same time. A qubit is also built around these two basic states. It cannot be both and it cannot be neither. At any time it is either in state 0 or state 1. Bits are pretty simple because they only have two possible states: 0 and 1. We use the word ‘state’ to describe what a bit, or qubit or whatever is doing. States and measurementsįirst, we need to give our simple little quantum objects a name. I should have said that they can be two things at once in a perfectly understandable and mathematically precise way. ![]() But they’ll also be able to be both at once in a weird and magical quantum way. Like a coin, that can be either heads or tails. These will only be able to do two possible things. To keep it as easy as possible, we’ll be thinking about the simplest kinds of quantum objects. ![]() In fact, it can be a lot easier than what we have to deal with in the non-quantum world sometimes. The basic maths of quantum mechanics isn’t all that hard. I’ll only use the kind of maths that people learn at school, and I’ll bear in mind that you’ve probably forgotten it all (and probably never understood it in the first place). I’m not saying that the maths in this post will be fun, but I’ll keep it as simple and painless as I can. But don’t be scared! Maths isn’t always scary. To do this, we are going to need some maths. So now it’s time to tell you the truth about quantum! I work on quantum stuff, and I’m a bit of an idiot. They make everything seem intangible, beyond the understanding of mere mortals and only to be dealt with by great sages. But such descriptions have serious drawbacks. I’m sometimes guilty of this exact same thing. Or maybe you heard it in Sci-Fi, where scientists treat equations like incantations that just need to be put it in a computer for magic to happen. Probably in a popular science article that called it weird and crazy, and didn’t tell you much else. I’m sure you will have seen the word ‘quantum’ before. Quantum Computation with the simplest maths possible ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |