The TRUE Difference Between a Quantum Computer and Your Home PC.

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Here's what you need in order to build a quantum computer: a bunch of qubits, and a way of keeping them all entangled and stable without decohering. But what does all of this even mean?

In this video, we start by understanding that classical computers are made from classical bits, or binary digits. These are basically switches that can be found in one of two positions. These positions can be labelled "0" and "1", or "TRUE" and "FALSE", or "YES" and "NO". The switches are physically made from transistors arranged in circuits within our computer in complicated and interesting ways.

Multiple bits together can be used to store information, using binary code. A simple version of this would be to store letters of the alphabet. Say our code was that 00001 = A, 00010 = B, 00011 = C, and so on. The positions of the transistor bits could be changed to reflect this. In addition to this, the changes in positions of these switches could be used to conduct computations and other functions a computer can undertake.

Now let's take our classical computer and make it quantum instead. To do this, we ditch our classical bits, and instead use quantum bits, or "qubits" for short. Qubits, when measured, can be found in either the "0" or the "1" state. However between measurements, the qubits can be in a "superposition" or blend of the two possible states. Another way of thinking about this is that the qubits can oscillate between the two possible states, which means at some points in time they will be between the two states. If we make a measurement when a qubit is in this superposition, then it will immediately flip to one of the possible measurement states. The probability with which it will flip to either one is given by how much of each state was "mixed" into the superposition.

The state of each qubit can be written using a wave function. The overall state can be written as a sum of the "0" and "1" states. There is also a number / amplitude at the front of each possible measurement state. If we find the square modulus of this number for a given state, we calculate the probability of finding our system in one of the possible result states.

The reason we need to take the square modulus is because the multipliers for each measurement state can actually be positive or negative, and even real or imaginary. In other words, these numbers are not restricted in any way and can even be complex. Complex numbers are formed by summing a real and an imaginary number. And naturally, if we find the square modulus of a complex number, we find a real, positive number. This is great because the square modulus represents a probability, which must be positive and real. The multipliers will also be essential for visualizing our qubits and their behavior in the next video within this mini-series!

Lastly, we look at how qubits are made in real life. We see two examples of two-state systems. Firstly, we study an atom with a single electron that can be found in one of two energy levels. Secondly, we look at a single electron, which has two spin states - spin up and spin down. These can also be relabeled as "0" and "1", meaning an electron can behave as a qubit. The difficulty in making quantum computers is in ensuring multiple qubits remain entangled together, and do not decohere due to external influences. This usually involves huge energy costs in cooling, and highly specialized environments.

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Timestamps:
0:00 - Classical Computers and Bits
1:25 - Quantum Bits (Qubits)
2:16 - Huge Thanks to Wren for Sponsoring This Video!
4:00 - Understanding Qubit Math (Wave Functions)
6:27 - Imaginary and Complex Numbers
9:10 - Real Life Examples of Qubits

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