 Before we begin today's lesson, it is worth noting some of the topics here do require a basic understanding of quantum theory and computing. So if you aren't too familiar with either one of those concepts, it's recommended you check out some of our other videos explaining those topics, as well as any reference material to help you out. And while we will discuss some topics in higher level math, we will not be going too in depth, as not all of you watching this may have a strong math background. With that being said, let's get right into it. Quantum Mechanics was pioneered by Werner Heisenberg, Max Born and Pascal Jordan in 1925, with their development of matrix mechanics, the first cohesive explanation of quantum mechanics. In the same year, Erwin Schrödinger published an equation which is used to describe the change over time of the state of a quantum mechanical system. In the 1980s, Richard Feynman began to consider the possibility of using quantum mechanics in computers. However, quantum computers remained purely theoretical for a long time. Peter Schor developed an algorithm to run on a quantum computer, which would break modern cryptographic techniques with ease. Since then, there has been a large amount of investment and research into quantum computing, in hopes that it can revolutionize fields like cryptography, artificial intelligence, computational chemistry, and finance. The simplest form of a quantum system is a single electron. Based on the Heisenberg uncertainty principle, we can never know the exact position or movement of an electron. We can only make probabilistic guesses. All future outcomes of some system are based on the amplitudes associated with that future state. Amplitudes are similar to probability, but they can also have negative or complex values. The power of amplitudes is that they can interfere with each other. Since normal probabilities can only be positive, there is no sense of cancelling out possibilities that we don't want. Based on the initial conditions of a quantum state, the amplitudes can act in such a way that certain amplitudes can interfere and completely cancel out. Superposition means that any two quantum states can be added together and will result in another valid quantum state. Equations for quantum computers, such as the one sure developed, exploit the phenomena of amplitudes, superposition, and interference. The quantum counterpart to a regular bit is the qubit. Whereas the classical bit can be either zero or one, qubits have a certain amplitude for being zero and a certain amplitude for being one. Of course, one bit or qubit doesn't mean much to us. If instead we have ten qubits, then we have to start accounting for different amplitudes for each of the qubits and then look at the combination of each of them. The algorithms specifically are used to manipulate amplitudes, such that through the summation of these amplitudes, some of the paths of the evolution of the qubits known to be wrong are not taken. It should be noted that any problem that can be solved with a quantum computer can be solved by a classical computer, given enough time and computing power. However, a problem that would take an infinite amount of time and power on a classical computer would have to take a reasonable amount of time on a quantum computer before the goal of quantum supremacy is achieved. Quantum supremacy is the point where a quantum computer can solve a problem many orders of magnitude faster than a classical computer, or maybe the classical computer cannot solve at all. For example, the vast majority of internet security is based on very large prime numbers which we assume are hard to find. However, with a quantum computer it will be exponentially easier to factor large numbers, and as a result find those very large prime numbers, rendering most of modern cryptography obsolete. The biggest problem with quantum computing is the idea of decoherence. A quantum state exists in the realm of amplitudes and possibilities, so as long as it's not measured. Schrodinger's Cat is a thought experiment which provides a visualization for this. If a cat is placed in a box with a 50% chance of dying, until the box is open, the cat is both alive and dead. The quantum state of the cat is isolated, so it does not have to localize into being either alive or dead. In terms of actual quantum computers, interference from the outside world, what quantum computer scientists call noise, can cause quantum states to localize before the algorithm is done running. This premature localization is called decoherence. While decoherence seems to be a fundamentally crippling problem, it was found that in order for a quantum computer to give back useful results, all the qubits did not have to be perfectly isolated from their surroundings. They simply had to be isolated well enough. Obviously, this is not a rigorous definition, but the idea of information entropy is similar to that which we deal with in regular systems of virtual networks, such as Wi-Fi, Ethernet, and Bluetooth. The quantum computing solution is the idea of self-correcting qubits. While continuously losing tiny amounts of information, all the qubits working in tandem are able to manipulate and transmit the data they need, nullifying the information loss of decoherence. Now the big question you probably have is, will you see people using quantum computers within the next few years? Most likely not, but there are great steps being taken towards the large scale implementation of quantum systems. The widespread use of these systems will usher in a new level of research into quantum mechanics, computational chemistry, and material science, among other fields. This video was just an intro to the subject for those who have had some basic background knowledge and we are definitely going to be diving into specific applications and challenges of quantum computing. Until then, stay tuned for more science videos.