The world is not classical in the sense of being continuous and deterministic. In fact, the opposite is the nature of the cosmos. Energy is not a continuous spectrum as we may have hypothesized. It all started with Bohr's atomic model which specified different energy levels. From this, physicists such as Richard Feymman have shown that there exists a very small amount of energy that cannot be further devided. It is the smallest amount of energy needed to move an electron between the layers, techincally it is measured from the energy released by an electron dropping an energy level. This is to say that energy is in fact discrete. What is this to say about determinism though. We think of determinism as the opposite of free will, when thats not really the best way to think about it in the context of what I am talking about here. Determinism means that given an action you can determine the result, in contrast stochasticism means that given an aciton you get a probability of having a result. An example of a stochastic environment would be the stock market, but at some level, it can be viewed as deterministic because everything happens because of something else. With advancements in quantum mechanics we have discovered a strange phenomenon existing in subatomic particles.
This strange quality is called the wave particle duality, and it is best demonstrated with the double slit expiriment. When we think of light, we either think of photons or waves. They exist in both states at the same time, and this can be shown in the double slit expiremnt because we can see the interference patterns from the waves that doesn't happen with particles. What is particularly interesting about this is its ties to observability, when we observe the photons going through the slits, they behave like particles. This is that factor of measurement that collapses the wave into a single position. Like these waves, some particles have a spin to them, or more accuratly a superposition of spins. A photon is either polorized up and down, or left to right when we observe it. But when it is unobserved it exists in a superposition of both probaiblites. This kind of probabilistic nature allows us to do calculations in a really different way. For example it lets us search an unsorted list in a speed thats propotional to the square root of the number of items. Also, we use things like the Quantum Fourier Transform in Shor's algorithm to factor really large numbers. A quantum computer takes advantage of these quantum principles.
One of the most interesting applicaitons of quantum computing are simulations. At the beginning of the blog, I made the claim that nature did not behave in accordance to classical mechanics. So to simulate nature, it should be done and probably will be done better when taking advantage of quantum propreties, the same quantum propreties that make up the nature we are simulating. This type of computing is inheritly probabilistic, that means that we cannot necessarily trust the answer 100% of the time, instead we do the same problem over and over again and learn from that probailty distribution, just like with the double slit expiriment. In fact we can still look at the double slit experiment to learn about quantum computation. Google this expirmiment real quick. Imagine we are trying to create a certain distibution of photons at the end, quantum computation would be choosing good ways to arrange multiple layers of slits at different distances to give a distibution. The wave function collapses at the end of the expirimet when we measure.
Another promising branch of quantum computing, and one that I am particularly interesed in is quantum machine learning (QML). One thing that quantum computers are really good at dealing with is computational complexity. Instead of bits in a classical computer, we deal with qubits in quantum computers. Qubits all connect to eachother which allows for the cool proprety of when you add one more qubit you double the computational power. This is a really good tool for the linear algebra part of deep learning. Something that might be introduced into computers someday is a quantum processing unit (QPU), analagous to the GPU and probably just as influential and changing in the field. Right now we are using quantum computers, or hypothesizing to use quantum computers to help with classical problems in deep learning.
One interesing and notable conneciton between these two feilds are optimization problems. Like I said earlier quantum particles behave stochasitaclly, according to a probabiltiy distribution of states that they could be in. Often times quantum physicists are trying to find some local minimum in a high dimensional energy. In the same fashion, deep learning engineers attempt to find the optimal solution in paramater space. When we have hundreds of paramaters inside of a neural network we use graident decent to approximate some local minimum describing how the system can accuratly generalize a phenomenon. Another way that quantum computation fit with machine learning is by creating probability distributions that classical models would resist. With this, we can help fix some of these loss probability distributions by creating a system of nets using deep quantum networks (DQNs) and deep neural networks (DNNs).