Here is an overview of essential knowledge regarding quantum gates.
Understanding |0⟩ and |1⟩:
|0⟩ (Ket Zero): This is one of the two fundamental states of a qubit. This is often called the ground state or the zero state. In physical terms, it represents the lowest energy state of a quantum system, similar to an electron in its lowest energy level in an atom.
|1⟩ (Ket One): The other fundamental state, known as the excited state or one state. This is similar to a higher energy state compared to |0⟩, like an electron excited to a higher energy level.
To Help Visualize: Imagine a sphere where |0⟩ is the north pole and |1⟩ is the south pole. Any other superposition would be somewhere on the sphere.
Quantum Gates
Pauli Gates:
X (NOT) Gate: Acts like a classical NOT gate, flipping ∣0⟩ to ∣1⟩ and vice versa.
Y Gate: This flips a qubit’s state similar to an X gate but also rotates it by 180 degrees around the Y-axis on the Bloch sphere.
Z (Phase Flip) Gate: Leaves ∣0⟩ unchanged but adds a phase to ∣1⟩.
Hadamard Gate (H): Creates superposition. It turns ∣0⟩ into (∣0⟩+∣1⟩)/sqrt(2) and ∣1⟩ into (∣0⟩−∣1⟩)/sqrt(2).
Phase Shift Gates (S, T):
S Gate (also known as the phase gate): Adds a 90-degree phase shift to ∣1⟩.
T Gate: A quarter-turn phase shift, this is useful for fine-tuning phases.
Controlled Gate:
CNOT (Controlled-NOT) Gate: If the control qubit is ∣1⟩, it flips the target qubit. Otherwise, it leaves the target unchanged.
Two-Qubit Gates (Beyond CNOT):
SWAP Gate: Exchanges the states of two qubits.
Controlled Phase Gate (CZ): Adds a phase to the target qubit if the control qubit is ∣1⟩.
This is a comprehensive list of all of the most common quantum gates and how they can be used. Understanding these will be essential to successfully designing quantum circuits.
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