From Classical to Quantum

What makes quantum computing fundamentally different from classical computing? This section breaks down the core concepts that separate the two worlds.

Classical Bits vs. Quantum Bits

Classical Bit

A classical bit is simple: it’s either 0 or 1. Period.

Classical bit: 0  OR  1

Every computer you’ve ever used processes information this way. Billions of transistors switching between two states.

Quantum Bit (Qubit)

A qubit can be 0, 1, or both at the same time.

Qubit: α|0⟩ + β|1⟩

This “both at the same time” is called superposition. The numbers α and β are complex numbers called amplitudes that describe the probability of measuring 0 or 1.

Important: When you measure a qubit, you get a definite answer (0 or 1). The superposition “collapses.” You can’t peek at the superposition directly.

The Three Pillars of Quantum Computing

1. Superposition

A qubit in superposition isn’t undecided. It’s genuinely in multiple states simultaneously. This allows quantum computers to explore many possibilities at once.

$$|\psi ⟩=\frac{1}{\sqrt{2}}|0⟩+\frac{1}{\sqrt{2}}|1⟩$$

This qubit has equal probability of being measured as 0 or 1.

Why it matters: With $n$ qubits, you can represent $2^n$ states simultaneously. 50 qubits can represent more states than a classical supercomputer can track individually.

2. Entanglement

When qubits become entangled, their states become correlated in ways impossible classically. Measure one, and you instantly know something about the other, regardless of distance.

The most famous entangled state is the Bell state:

$$|{\Phi }^{+}⟩=\frac{1}{\sqrt{2}}(|00⟩+|11⟩)$$

Both qubits are in superposition, but they’re perfectly correlated: if you measure the first as 0, the second will also be 0. Measure 1, and the second is 1.

Why it matters: Entanglement is a resource for quantum computation and communication. It enables quantum teleportation, superdense coding, and is essential for quantum speedups.

3. Interference

Quantum states can interfere with each other, like waves in water. Amplitudes can add (constructive interference) or cancel (destructive interference).

Why it matters: Quantum algorithms are designed to make wrong answers interfere destructively and right answers interfere constructively. This is how you extract useful results from quantum computation.

How Quantum Computation Works

A quantum computation follows this pattern:

1. INITIALIZE: Prepare qubits in a known state (usually |0⟩)
2. SUPERPOSE: Put qubits into superposition (using Hadamard gates, etc.)
3. ENTANGLE: Create correlations between qubits (using CNOT gates, etc.)
4. COMPUTE: Apply quantum gates that cause interference
5. MEASURE: Read out the final answer

The art of quantum algorithm design is arranging steps 2-4 so that interference amplifies correct answers and suppresses wrong ones.

What Quantum Computers Are NOT

Common myths:

NOT exponentially parallel classical computers: You can’t just run all possible inputs simultaneously and read all outputs. Measurement gives you ONE result.

NOT instantaneous: Quantum operations take time, and quantum algorithms have complexity like classical ones.

NOT universally faster: Only specific problems have known quantum speedups. For many tasks, classical computers are just as good or better.

NOT breaking physics: Entanglement doesn’t enable faster-than-light communication. You need classical communication to use quantum correlations.

When Quantum Computers Help

Quantum computers excel at specific problem types:

*With caveats about input/output

Key Intuition

Think of quantum computing like this:

Classical computing is like reading a book page by page.

Quantum computing is like having a book where all pages exist in superposition, and through careful manipulation, you can make the page you’re looking for “pop out” with high probability.

The challenge? Designing that “careful manipulation.” Most of the pages you don’t want need to interfere destructively, while the answer constructively builds up. This is genuinely hard, which is why useful quantum algorithms are rare and precious.

Now you have the conceptual foundation. Head to the Acronyms for quick reference, or dive into specific definitions to explore further.