Quantum Computing
Quantum Computer —
The Future of Computing
A classical computer operates with bits — 0 or 1. A quantum computer uses qubits, which can be both 0 and 1 simultaneously. This fundamental difference gives computational power that is inaccessible to classical computers.
2ⁿ
states for n qubits
256
states in 8-qubit quantum byte
1000+
qubits — IBM Condor (2023)
10⁶×
speedup in Grover's algorithm
01 — Quantum Bit
Qubit — The Basic Unit of Computation
A classical bit is always exactly 0 or 1. A qubit, through the quantum mechanics principle of superposition, exists in both states simultaneously until measured.
Classical Bit
b ∈ {0, 1}
Always exactly 0 or 1. One bit = one definite state.
Qubit — General Notation
|ψ⟩ = α|0⟩ + β|1⟩
α and β — complex amplitudes. |α|² + |β|² = 1. Measurement yields 0 or 1.
Equal Superposition
|+⟩ = (|0⟩ + |1⟩)/√2
50% probability for each state. The Hadamard gate creates this state.
Bloch Sphere
|ψ⟩ = cos(θ/2)|0⟩ + e^{iφ}sin(θ/2)|1⟩
Any qubit state is a point on the unit sphere surface. θ — polar angle, φ — azimuthal.
Concrete Example — Writing a Qubit
Physically, a qubit can be: electron spin (↑=|0⟩, ↓=|1⟩), photon polarization (→=|0⟩, ↑=|1⟩), superconducting circuit (current direction), or an ion energy level.
|0⟩ = [1]
[0]
|1⟩ = [0]
[1]
|+⟩ = 1/√2 · |0⟩ + 1/√2 · |1⟩ = [1/√2]
[1/√2]
|ψ⟩ = 0.6·|0⟩ + 0.8·|1⟩
02 — Quantum Register
Quantum Byte and n-Qubit Register
n qubits exist simultaneously in 2ⁿ superposition states. 8 qubits (quantum byte) — 256 states. 300 qubits — 2³⁰⁰ states, more than the number of atoms in the observable universe.
| Qubits |
States |
Classical Equivalent |
Example |
| 1 | 2¹ = 2 | 1 bit | |0⟩, |1⟩ |
| 2 | 2² = 4 | 2 bits | |00⟩, |01⟩, |10⟩, |11⟩ |
| 3 | 2³ = 8 | 3 bits | |000⟩ ... |111⟩ |
| 8 | 2⁸ = 256 | 1 byte | Quantum byte |
| 32 | 2³² ≈ 4×10⁹ | 4 GB memory | — |
| 300 | 2³⁰⁰ ≫ 10⁸⁰ | More than atoms in universe | — |
|Φ⁺⟩ = 1/√2 · (|00⟩ + |11⟩)
|GHZ⟩ = 1/√2 · (|000⟩ + |111⟩)
Quantum Entanglement
Entangled qubits share a "magical" connection regardless of distance. Measuring one qubit instantly determines the other's state. Einstein called this "spooky action at a distance." This does not mean information travels faster than light — a classical channel is still needed.
03 — Architecture
Quantum Circuit and Gates
Quantum computation is written as circuits: qubits are lines, gates are operations. Gates are unitary matrices that transform the qubit state.
X (NOT)
|0⟩→|1⟩, |1⟩→|0⟩
[[0,1],[1,0]]
H (Hadamard)
|0⟩→|+⟩, superposition
1/√2 · [[1,1],[1,-1]]
Z (Phase)
|0⟩→|0⟩, |1⟩→-|1⟩
[[1,0],[0,-1]]
CNOT
2-qubit, entanglement
|c,t⟩ → |c, c⊕t⟩
T (π/8)
Phase rotation by π/4
[[1,0],[0,e^{iπ/4}]]
Toffoli (CCNOT)
3-qubit, universal
|a,b,c⟩→|a,b,c⊕ab⟩
q0: ──H──●────
│
q1: ─────X────
|00⟩
1/√2(|00⟩ + |10⟩)
1/√2(|00⟩ + |11⟩) = |Φ⁺⟩
04 — Challenges
Decoherence — The Main Challenge
A qubit loses its quantum state very quickly due to interaction with the environment. This is the most significant practical problem of quantum computing.
⏱️
Coherence Time
Superconducting qubit: ~100μs. Ion trap: ~1 second. All quantum operations must complete within this time.
❌
Quantum Errors
Gate error rate: ~0.1-1%. Classical computer: ~10⁻¹⁸. Quantum error correction requires 1000+ physical qubits for 1 logical qubit.
🌡️
Temperature
Superconducting quantum computers operate at ~15 mK (-273.135°C) — among the coldest places in the universe. This is 180 times colder than outer space (2.7 K).
🛡️
Error Correction
Surface Code — most popular approach. 1 logical qubit requires ~1000 physical qubits. Google and IBM are actively working in this direction.
05 — Quantum Advantage
Quantum Algorithms and Real Examples
Quantum computers are not faster at every task. They provide special advantage in specific classes — optimization, cryptography, simulation.
🔢
Shor-ის ალგორითმი (1994)
Integer factorization in polynomial time. Breaks RSA encryption. ~4000 logical qubits needed to break 2048-bit RSA.
🔍
Grover-ის ალგორითმი (1996)
Search N elements in √N steps (classically N/2). Searching 1 million elements: classical — 500,000 steps, quantum — ~1,000.
⚗️
Quantum Simulation
Simulation of molecules, materials, chemical reactions. Classically, 50+ atom systems are practically impossible. Penicillin, new materials, pharmaceuticals.
🌐
Google Sycamore (2019)
53-qubit processor solved in 200 seconds a task that would take a classical supercomputer 10,000 years. First demonstration of "quantum advantage."
🏦
Quantum Optimization
Logistics, financial portfolio, routing. D-Wave annealing with 5000+ qubits. Practical industrial applications.
🔐
Post-Quantum Cryptography
NIST approved the first post-quantum standards in 2024 (CRYSTALS-Kyber, CRYSTALS-Dilithium) — encryption resistant to quantum computers.
06 — Physical Architecture
Types of Quantum Computers
The physical realization of a qubit can be achieved through various technologies. Each has its own advantages and disadvantages.
🔵
Superconducting Qubit
IBM, Google, Rigetti. 15 mK. Fast gates (~10-50 ns). Short coherence. Scalability: currently most promising.
⚡
Ion Trap
IonQ, Honeywell. Room temperature (vacuum). Long coherence (~1 s). Slow gates (~1-10 μs). High fidelity.
💡
Photonic Qubit
PsiQuantum, Xanadu. Room temperature. Speed of light. Networking. Quantum internet. Less coherence problem.
💎
NV Center (Diamond)
Room temperature. Nitrogen-vacancy in diamond. Quantum sensor, biological applications. Quantum memory.
07 — Interactive Modules
Simulators and Visualization
In the future, this platform will feature an interactive quantum circuit simulator, Bloch sphere visualization, and step-by-step demonstrations of quantum algorithms.
SOON
⚛️ Quantum Circuit Simulator
Qubits, gates, measurement — visually
SOON
🌐 Bloch Sphere Visualization
Qubit state in 3D, rotations
SOON
🔢 Shor's Algorithm — Step by Step
Factorization with quantum circuit
SOON
🔍 Grover's Search
Quadratic speedup with visualization
SOON
📊 Quantum Noise Simulator
Decoherence and errors
SOON
🔐 BB84 Quantum Cryptography
Quantum key distribution