Quantum Computing Fundamentals

Explore quantum algorithms, qubit manipulation, and quantum supremacy concepts through interactive visualizations.

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What is Quantum Computing?

Quantum vs Classical Computing

Quantum computing leverages quantum bits (qubits) that can exist in superposition states and become entangled, enabling exponential computational power for certain problems.

Qubits

Quantum bits that can represent both 0 and 1 simultaneously through superposition

Entanglement

Linked states where quantum information is instantaneously connected between qubits

Gates

Quantum operations that manipulate qubit states using matrices

Core Concepts

Qubit Representation

A qubit can be represented as a vector in a two-dimensional complex Hilbert space: $ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $ where $ |\alpha|^2 + |\beta|^2 = 1 $

State Visualization

Superposition Circle

Each point on the circle represents a valid qubit state

Qubit States

  • |0⟩ state at (1,0)
  • |1⟩ state at (0,1)
  • |+⟩ state
  • Entangled states

Basis States

Quantum computing uses orthonormal basis states to construct superpositions and perform quantum measurements.

$$ \mid\psi\rangle = \frac{1}{\sqrt{2}} (|0\rangle + |1\rangle) $$
Superposition state
|0⟩
Base state with coefficient 1
|1⟩

|1⟩ state vector

Quantum Gates

Quantum logic gates transform quantum states using unitary matrices. Commonly used gates include the Hadamard, Pauli gates, and the CNOT gate.

Hadamard Gate

|0⟩ → (|0⟩ + |1⟩)
|1⟩ → (|0⟩ - |1⟩)
                        
H = 1/√2 * [[1, 1],
            [1,-1]]

CNOT Gate

Controlled operations that manipulate entangled qubits

Applies a NOT to the second qubit when the first qubit is |1⟩

CNOT |1,0⟩ → |1,1⟩ → |1,1⟩

Toffoli Gate

3-qubit gate: Control-1

Conditional operation on 3 qubits

|a,b,c⟩ → a|b,c⟩

Applications

Quantum Chemistry

Simulate molecular structures and chemical reactions that are intractable for classical computers.

  • • Quantum simulation of molecular dynamics
  • • Drug discovery and material science applications
  • • Quantum simulations
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Quantum Security

Quantum algorithms can break traditional encryption methods like RSA with Shor's algorithm.

Algorithm Impact Security
Shor's Algorithm Efficient integer factorization Breaks RSA
Grover's algorithm
Unstructured search
 Reduces search to sqrt(N)

Learn more about post-quantum cryptography

Quantum Simulations

Experience quantum phenomena and operations firsthand with our interactive simulator.

Quantum Computing Concepts

Quantum Gate Operations
Quantum Circuits
Quantum Algorithms
Drag and drop quantum gates to create circuits.
Quantum Algorithm Steps:
1. Initialize qubit states
2. Apply operations
3. Measure results

Try it live

Create and test quantum circuits with real-time simulation feedback.

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Open-source Quantum Experiments

Access and contribute to community-created quantum computing simulations and experiments.

Shor's Algorithm

Quantum Fourier Transform

Quantum Fourier Transform

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Quantum Fourier Transform

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