2.1 Quantum bits ‣ Quest 2: Conqueror of the qubit ‣ The Quantum Quest‣ Quest 2: Conqueror of the qubit ‣ The Quantum Quest

Bits are the basic units of information in our current-day computers. To realize a bit, you need a physical object that can be in one of two reliably distinguishable states, such as a coin with two sides or a capacitor storing electric charge at two different possible voltage levels.⁷⁷ 7 This is essentially the way that bits are represented in your computer, mobile phone, etc. The behavior of such objects (and hence the bits they encode) can be described by physical theories such as mechanics (for coins) or electromagnetism (for capacitors).

However, for really tiny⁸⁸ 8 By “really tiny” we mean really, really tiny! If you would put electrons next to each other in a line, the number of electrons you would need to reach the length of 1 cm is similar to the number of pages you would need to put on top of each other to reach the Moon. objects these theories no longer apply and you have to use a more fundamental theory called quantum mechanics. For example, an electron has a property called spin, which (just like a coin) can take one of two values – up or down – and hence can be used to store a bit. However, unlike a coin, electron’s spin may not be just in one of these two states but also in a “superposition” of both! Intuitively, this is somewhat similar to a probabilistic bit that can also be in an intermediate state between $0$ and $1$ .

However, there is a subtle difference between probabilities and “superpositions” (see Section 2.6.1 on interference). As we will see, the laws of quantum mechanics lead to a much more fundamental notion of information than a bit – a quantum bit or qubit. To distinguish the usual bits from their more exotic quantum friends, we will call the usual bits classical.

We will define quantum bits using a simple mathematical model and not worry about how their strange behavior should be interpreted but instead ask the question: “What can it be used for?”. Similarly, we will also not worry about how they can be implemented physically or what kind of physical objects can be used to store them. However, if you are curious about this, we briefly discuss in Section 2.6.2 how polarization of light can be used to represent a qubit.