Operations on the qubits:

    Like the AND and OR gates in classical computing, in quantum computing there are a special set of gates known as the quantum logic gates which we use to perform quantum operations or effects on the qubits.

CNOT Gate/Operation:

The CNOT operation (Controlled NOT) is a fundamental quantum logic gate that operates on two qubits, one designated as the control qubit and the other as the target qubit. It performs the following operations:
a) If the control qubit is in the state |1⟩, the target qubit is flipped (i.e., its state changes from |0⟩ to |1⟩ or vice versa).
b) If the control qubit is in the state |0⟩, the target qubit remains unchanged.
CNOT gate is necessary for entagling and disentangling qubits. This helps to perform complex quantum computation.

Hadamard Gate:

The Hadamard gate is a fundamental quantum gate in quantum computing that creates superposition states of a qubit. It transforms a qubit from a definite state (|0⟩ or |1⟩) into a superposition of both states, allowing for the simultaneous existence of multiple quantum states.

The Hadamard gate is represented by the matrix:
H = 1/√2 [1 1 1 -1]
When applied to |0⟩, it produces (|0⟩ + |1⟩)/√2, and when applied to |1⟩, it produces (|0⟩ - |1⟩)/√2. This ability to create superposition is crucial for many quantum algorithms and is often the first gate applied in quantum circuits.

Pauli-X Gate:

    The Pauli-X gate, commonly referred to as the bit-flip gate, operates on a single qubit and functions as a “quantum NOT gate.”It is similar to the classical NOT gate used in traditional computing. In Classical computing, a NOT gate inverts a binary bit, turning 0 into 1 and 1 into 0. Similarly, the Pauli-X gate reverses the state of a qubit, transforming |0⟩ into |1⟩ and |1⟩ into |0⟩.

Pauli-Z Gate:

   The Pauli-Z gate, commonly referred to as the phase-flip gate, inverts the relative phase of these state without altering the base states.To put it simply, the Pauli-Z gate alters a fundamental property of quantum physics known as the “phase” of the qubit’s state.The Pauli-Z gate transforms the state |0⟩ to |0⟩ and the state |1⟩ to -|1⟩.

Pauli-Y Gate:

   The Pauli-Y gate acts on a single qubit. It performs both bit-flip (as the Pauli-X Gate) and phase-flip (as the Pauli-Y Gate) on a single qubit. The Pauli-Y gate transforms the state |0⟩ to -i|1⟩ and the state |1⟩ to i|0⟩.