Hadamard gate puts a qubit into equal superposition of |0⟩ and |1⟩
Quantum logic gate
Hadamard gate puts a qubit into equal superposition of |0⟩ and |1⟩
The Hadamard gate is a fundamental quantum logic gate that transforms a qubit into a superposition of states. This transformation is essential for quantum computing as it allows qubits to exist in multiple states simultaneously, enabling parallel computation.
Example
Applying the Hadamard gate to the |0⟩ state results in the superposition (|0⟩ + |1⟩)/√2. This means the qubit is now equally likely to be measured as |0⟩ or |1⟩.
Understanding the Hadamard gate's function is crucial for grasping how quantum superposition enables the power of quantum computing.
Related concepts
Quantum superposition
A qubit exists in superposition of |0⟩ and |1⟩
Shor's algorithm
Shor's algorithm factors integers in polynomial time on a quantum computer
quantum entanglement means: measuring one qubit instantly determines the other's state
Quantum entanglement means: measuring one qubit instantly determines the other's state
Quantum computing
Quantum computers can solve certain problems exponentially faster than classical computers
QR decomposition
QR decomposition factors A = QR, where Q is orthogonal, R is upper triangular
the condition number κ(A) measures: sensitivity of Ax=b to perturbations
The condition number κ(A) measures the sensitivity of Ax=b to perturbations
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