Most of the digital security we rely on today is based on a simple but powerful mathematical idea: while it is easy to multiply two very large prime numbers together, it is practically impossible for a classical computer to reverse the process and find those original prime factors.

Imagine a simple problem: you are given a black box, or oracle, containing a function $f$ that takes a single bit as input and returns a single bit as output.

What if you wanted to scale up the problem from Deutsch's algorithm?

In this Quantum Computing: From Concepts to Code's chapter, we'll solve a new type of promise problem using a circuit that looks exactly like the one we used for the Deutsch-Jozsa algorithm.

Imagine a bizarre promise oracle that contains a secret bitstring, $s$, of length $n$.

In quantum teleportation, the goal is not to move matter, but to instantly transfer the quantum state of one qubit to another, seemingly over any distance.

In classical programming, the first program many of us learn is 'Hello, World!

A single qubit, like a single bit, can't accomplish much on its own.

When we assemble multiple qubits into a single system, they often form a special relationship called entanglement.

In classical computing, the outcome of any program is entirely predictable.

At its heart, a qubit is not just a 0 or a 1.

Just as the classical computer is built on the bit, the core of quantum programming is the qubit.

A quantum computer is a linear computer, meaning that all of its underlying operations are based on linear algebra.

Just as classical computers use logic gates like AND and OR to manipulate bits, quantum computers use quantum gates (qugates) to manipulate qubits.

When you hear the term quantum computing, it might sound exotic, but what does it actually mean for a computer to be 'quantum'?