What are quantum gates? How do they differ from classical logic gates?

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Quantum gates are the building blocks of quantum circuits, similar to how classical logic gates form digital circuits. They are operations applied to qubits that change their state by manipulating probabilities and phases. Mathematically, quantum gates are represented as unitary matrices that ensure reversibility and preserve the total probability of the quantum system.

For example:

• The Pauli-X gate acts like a classical NOT gate, flipping |0⟩ to |1⟩ and vice versa.

• The Hadamard (H) gate creates superposition, turning |0⟩ into (|0⟩ + |1⟩)/√2.

• The CNOT gate (Controlled-NOT) is a two-qubit gate that flips the target qubit only if the control qubit is |1⟩, enabling entanglement.

Difference from classical logic gates:

1. Reversibility – Classical gates like AND/OR lose information and are irreversible, while quantum gates are always reversible due to unitarity.

2. Superposition – Classical bits are either 0 or 1, but qubits can exist in both simultaneously. Quantum gates can manipulate these superpositions.

3. Entanglement – Quantum gates can create correlations (entanglement) between qubits that have no classical counterpart.

4. Parallelism – A quantum gate operating on a superposition effectively processes multiple states at once, enabling quantum parallelism.

5. Representation – Classical gates use Boolean algebra, while quantum gates use linear algebra with complex numbers.

In short, while classical gates process definite 0s and 1s, quantum gates exploit superposition and entanglement, making them far more powerful for certain computations like factoring or searching.

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