Understanding
Quantum
Computers

Foundations

Bits and Qubits

A classical computer processes information in binary: each bit is either 0 or 1. A quantum computer uses qubits, which behave very differently.

The classical bit

In a classical system, a bit is like a light switch — definitely on or definitely off. Every computation is a deterministic sequence of bit flips following Boolean logic. The power of classical computers comes from performing billions of these simple operations per second.

The qubit: superposition

A qubit (quantum bit) can exist in a superposition of 0 and 1 simultaneously — not in a fuzzy "half-on" sense, but as a coherent quantum state described by a probability amplitude. Only when you measure a qubit does it collapse to a definite 0 or 1.

This doesn't mean a qubit "is both at once" in a classical sense. It means the qubit's state is a complex linear combination |ψ⟩ = α|0⟩ + β|1⟩, where |α|² + |β|² = 1. The amplitudes α and β encode interference relationships, which is where the computational power hides.

Entanglement

Quantum entanglement links multiple qubits so their states cannot be described independently. Two entangled qubits in the Bell state (|00⟩ + |11⟩)/√2 are correlated: measuring one instantly determines the other, regardless of distance. For computation, entanglement is a resource that creates correlations across all qubits in a register, enabling certain algorithms to explore an exponentially large space of possibilities in a structured way.

Quantum interference

Quantum algorithms are designed to make amplitudes of wrong answers cancel each other (destructive interference) while amplitudes of right answers reinforce (constructive interference). This is the mechanism by which quantum algorithms accelerate computation — not raw parallelism.

Computation model

Quantum Gates and Circuits

Quantum computation is performed by applying quantum gates — unitary transformations that rotate qubit states on the Bloch sphere. Unlike classical gates, quantum gates are reversible (unitary matrices), which is a fundamental constraint.

Common single-qubit gates

• Hadamard (H) — creates superposition: maps |0⟩ to (|0⟩+|1⟩)/√2. Used to initialize qubits for parallel exploration.
• Pauli-X — the quantum NOT gate; flips |0⟩ ↔ |1⟩.
• Phase gates (T, S) — add relative phase to |1⟩ without changing measurement probability. Critical for interference engineering.

Two-qubit gates

• CNOT (Controlled-NOT) — flips the target qubit if the control qubit is |1⟩. Essential for creating entanglement.
• Toffoli (CCNOT) — doubly-controlled NOT; provides universal classical computation within a quantum circuit.

Circuit depth and quantum complexity

A quantum algorithm is expressed as a circuit: a sequence of gates acting on a register of qubits, ending with measurements. The depth (number of sequential gate layers) must stay low enough that decoherence doesn't destroy the quantum state before the circuit finishes. This is the central engineering challenge.

Hardware landscape

Quantum Computing Platforms

Several physical approaches to building qubits are under active development. Each has distinct trade-offs in qubit count, coherence time, gate fidelity, and connectivity.

Error correction

Physical Qubits vs. Logical Qubits

Every physical qubit is noisy. Gates have error rates of 0.1–1%. Qubits decohere — they lose their quantum state to the environment — within microseconds to milliseconds depending on the platform. Running a long algorithm on noisy qubits produces garbage.

Quantum Error Correction (QEC)

Quantum error correction encodes one logical qubit in many physical qubits. The surface code, the leading QEC scheme, requires roughly 1,000–10,000 physical qubits per logical qubit depending on gate error rates. A circuit of L logical operations needs logical qubits with error rate < 1/L.

What does "cryptographically relevant" mean?

Breaking RSA-2048 with Shor's algorithm requires approximately 4,000 logical qubits and ~10⁸ logical gates, per the landmark Gidney & Ekerå (2021) analysis. Translating to physical qubits with current surface-code overhead means roughly 20 million physical qubits at error rates near 10⁻³, or ~4 million at 10⁻⁴.

Today's best machines (IBM Heron: 133 qubits; Google Willow: 105 qubits; IonQ Forte: 36 algorithmic qubits) are 5–6 orders of magnitude away from this threshold. However, progress has been rapid and non-linear.

Timeline

When Could a CRQC Arrive?

A Cryptographically Relevant Quantum Computer (CRQC) is one capable of running Shor's algorithm to break RSA-2048 in a reasonable time. Estimates vary widely.

The wide range reflects genuine scientific uncertainty. What is certain is that the migration of large enterprise IT estates takes 5–10 years, and that adversaries harvesting traffic today face no deadline — they wait as long as needed.