Quantum gates and circuits
Hadamard gate
Definition (https://www.quantum-inspire.com/kbase/hadamard/)
The Hadamard gate is a single-qubit operation that maps the basis state ∣0?∣0? to ∣0?+∣1?22∣0?+∣1? and ∣1?∣1? to ∣0??∣1?22∣0??∣1?, thus creating an equal superposition of the two basis states.
Quantum Circuit
A quantum circuit is a network of quantum gates followed by a quantum measurement element and linked by wires where these gates perform some unitary operators on 1?qubit or n?qubits (wires).
Pauli X Gate (single Qubit)
Pauli Gates
These gates work by changing the direction of the vector ∣ψ? in either the x, y or z direction.
Quantum circuits are a way to design and visualize quantum algorithms. They help researchers and engineers plan and implement quantum computations by specifying the sequence and arrangement of quantum gates. These circuits can become quite complex for solving certain problems, and quantum circuit design is a crucial part of quantum computing research and development.
It's important to note that quantum circuits can leverage the unique properties of quantum mechanics, such as superposition and entanglement, to solve certain problems more efficiently than classical computers. However, building and maintaining quantum circuits are significant challenges due to the delicate nature of quantum information and the need for error correction to mitigate the effects of noise and errors in quantum hardware.