The qubit and the quantum computer

From bit to qubit

A classical computer manipulates bits: each is 0 or 1. A quantum computer manipulates qubits (quantum bits), which exploit superposition: a qubit can be 0, 1, or any superposition a|0⟩ + b|1⟩.

   Classical BIT :   0   or   1          (two possible values)

   QUBIT :           a|0⟩ + b|1⟩          (a continuum of superpositions)

A single qubit works no miracle. The power comes from the number of qubits combined with entanglement.

The exponential explosion

Here is the idea behind the whole appeal of quantum computing. With n classical bits, you represent only one combination at a time. With n qubits entangled in superposition, you manipulate all 2^n combinations simultaneously:

   n qubits  ->  2^n states in superposition at the same time

     n = 10  ->  2^10  = 1 024 states
     n = 20  ->  2^20  ≈ 1 million
     n = 50  ->  2^50  ≈ 10^15 (a thousand trillion)
     n = 300 ->  2^300 > number of atoms in the observable universe

With only 300 qubits, you manipulate more states than there are atoms in the universe. It is this massive parallelism that makes some computations, impossible for a classical computer, conceivable.

Watch out for the misunderstanding

This parallelism does not mean a quantum computer "tries all the answers and picks the right one" as if by magic. The trap: in the end, you have to measure, and the measurement returns only one result, at random. The whole difficulty of a quantum algorithm is to orchestrate the superpositions and the interference so that the right answer comes out with a high probability, and the wrong ones cancel out.

   bad idea :  "it computes everything and I read everything"   -> WRONG
   reality  :  clever interference -> the right
               answer has a high probability at measurement

What it is good for (and what it is not good for)

Quantum computers are not classical computers "but faster" for everything. They excel at a few very specific problems:

• factoring large numbers (Shor's algorithm) — which would threaten current RSA encryption;
• searching an unsorted database (Grover's algorithm);
• simulating molecules and quantum materials (chemistry, pharmacy) — their most promising application.

For office work, the web or games, a classical computer remains far better suited.

The great challenge: decoherence

The main obstacle is the one seen in the previous chapter: decoherence. The qubits must stay in superposition long enough to compute, which demands extreme isolation (temperatures close to absolute zero, shielding). The slightest interaction with the environment destroys the quantum information. This is why, despite spectacular progress, the universal quantum computer remains a major engineering challenge.

In summary

The qubit generalizes the bit thanks to superposition. With n entangled qubits, you manipulate 2^n states at once — an exponential growth that, by just 300 qubits, exceeds the number of atoms in the universe. But the measurement returns only one result: a good quantum algorithm makes the states interfere to bring out the right answer. These machines excel at targeted problems (factoring, quantum simulation), at the cost of a constant fight against decoherence.