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Quantum Computing From a Computer Science Perspective
When approaching quantum computing from a computer science perspective, it may seem intuitive to begin by comparing quantum computers directly with their classical counterpart. However, many who attempt to learn this way (myself included) end up more confused than informed, especially after encountering the complex mathematical and physics notation present in popular literature.
When approaching quantum computing from a computer science perspective, it may seem intuitive to begin by comparing quantum computers directly with their classical counterpart. However, many who attempt to learn this way (myself included) end up more confused than informed, especially after encountering the complex mathematical and physics notation present in popular literature. Instead, we will assume a basic understanding of how classical computers function, and discuss the unique qualities of a quantum computation separately. Although this distinction is a subtle, a quantum-focused approach is arguably more enlightening than a direct comparison.
It is worth noting that this is a difficult subject, and thus we encourage beginners to surround themselves with a healthy mix of both literature and examples (see the Activity Corner for additional resources). Understanding quantum state takes time and effort, and it's normal to be confused when starting out. As Richard Feynman said:
"Nature isn't classical . . . and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy."
We can think of a biased coin as a probabilistic bit — i.e. there is some randomness to the result, as opposed to deterministically measuring 0 and 1. The probabilities associated with each outcome can be thought of as the parameters of a random process before sampling it, similar to a spinning coin before landing on one of its sides. When the number of possible outcomes is greater than one, we refer to the state as being in superposition of those outcomes. While this term is often used in quantum computing, this idea is not unique and exists for any probabilistic system.
A quantum bit (abbreviated qubit or qbit) is a generalized version of the probabilistic bit. Instead of associating probabilities with each outcome (as we do in the probabilistic bit), we associate 2-dimensional vectors or arrows, which are called amplitudes. The probabilities of the outcomes are correlated to the magnitudes of their corresponding amplitudes. More precisely, the probability of an outcome is the square of the length of its corresponding arrow. Therefore, we can use arrows to represent each outcome of a qubit.
We don't discuss the outcomes of each individual coin (or qubit) separately. Each face corresponds to a possible combination of heads or tails and has its own probability of being measured. When all outcomes are equally likely to be measured (like in this example), we define the state as being in equal superposition. While equal superposition has its uses (e.g. sampling), typically we want to eliminate some of the possible outcomes, the details of which are problem-specific.
Using the example of a quantum die, let's assume we only want the die to return one of two results: 00 or 11. In a quantum system this can be done with entanglement. Specifically, we force one qubit's measurement to match the other, eliminating the outcomes 01 and 10. The result is effectively a fair coin — there is a 50/50 chance of measuring 00 or 11, which can be classically post-processed into heads (0) or tails (1).
Working with a quantum system is similar to playing a slot machine. We have a desired outcome (or event), a series of operations we are allowed to perform on the qubits and a limited number of available qubits to work with. The challenge is to construct a quantum state that gives the desired answer in the least amount of measurements, which manifests as a balance between accuracy and computation time.
A state in superposition is like a spinning coin or a cast die. Because the coin has yet to stop spinning (or the die has yet to land on a face), more than one outcome is possible. This is sometimes called a general superposition. States can also be in equal superposition (all outcomes are equally likely - the coin is fair, the die is unbiased, etc.).
If we have a spinning, biased coin, we have a general superposition (there are two possible outcomes, but one is more likely than another). If we have a spinning, fair coin, we have an equal superposition (all outcomes are possible, and they are equally likely to be measured). Note that an equal superposition is just a general superposition with an additional equality constraint.
The first part of Foundational Patterns for Efficient Quantum Computing details a visual approach to quantum computing, from which this article was derived.
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