Tutorial

#### From Bits to Qubits

Qubits, or quantum bits, are the equivalent of classical bits that drives quantum computing. But, unlike their classical counterparts, quantum bits are tricky to describe. Almost all textbooks, articles or explainer videos immediately jump to math to define qubits as if the key to understanding them lies in unraveling abstruse equations. The usual approach makes quantum computing feel as an alien landscape for most computer programmers even though it’s applied to traditional computational tasks. Without properly motivating the intuition quantum mechanics brings to bear, designing algorithms that capitalize on them to solve hard problems that are out of reach of today’s computers, is frustrating.

Although the behavior of quantum bits are governed by quantum mechanics, from a quantum computing standpoint, their actions can be boiled down to commonplace operations. To fix ideas, I use a pentagon for a $\ket{0}$ qubit:

And, a triangle for a $\ket{1}$ qubit:

We'll call these shapes qubelets. So we'll call the pentagon shape represeting a $\ket{0}$ qubit a $\ket{0}$ qubelet. Likewise a triangle $\ket{1}$ is called a $\ket{1}$ qubelet.

When these shapes represent classical bits, their orientations are always fixed.

With quantum bits, these shapes rotate. For example, a triangle $\ket{1}$ qubelet that's rotated, say, $45^{\circ}$ anti-clockwise is shown below:

A triangle $\ket{1}$ qubelet rotated $180^{\circ}$ so that it's upside down is:

This qubit is mathematically written with a negative sign $-\ket{1}$.

This ability of a quantum bit to rotate is the first difference from a classical bit. Pairs of qubelets, in which one is rotated $180^{\circ}$ from the other, cancel out and are removed from the quantum state. This behavior has no classical equivalent. This seemingly minute difference plays a pivotal role in making quantum computers so much more powerful than classical computers.

Another difference between a qubit and a classical bit that leads to hyper-fast computations is the ability of qubits to be in two states at the same time. That is, their ability to be suspended in a superposition of both $\ket{0}$ and $\ket{1}$ states.

What does this really mean? How can something be two things at the same time?

You may have heard of Schrödinger's cat in a closed box. Someone outside the box wouldn't have a clue whether the cat is dead or alive. So, for this person, their lack of knowledge allows them to think of the cat as being in two states — dead or alive. It's only when the box is opened would they know if the cat is breathing.

This concept of superposition sounds thrilling but it's not apparent how it could solve problems. So how exactly does one go about making any sense of superposition when designing a computer algorithm to solve a real world application?