A quantum circuit is a model used in quantum computing to represent the flow of quantum information through a sequence of quantum gates. A quantum gate is a unitary operation that can act on one or more qubits (quantum bits) to manipulate their quantum states. In a quantum circuit, qubits are represented as wires, and quantum gates are represented as boxes that act on the wires.
The circuit is typically drawn from left to right, with the input qubits on the left and the output qubits on the right. Quantum circuits are used to perform quantum algorithms and simulations. They are also used to implement quantum error correction codes and to design quantum hardware.
Quantum gates
Quantum gates are fundamental building blocks of quantum circuits. They are analogous to the classical logic gates used in classical digital circuits, but instead of operating on classical bits (which can be either 0 or 1), quantum gates operate on quantum bits or qubits, which can exist in superpositions of 0 and 1.
Quantum gates are represented by unitary matrices, which are reversible and preserve the normalization of the quantum state. There are several types of quantum gates, including:
1. Pauli gates: These are single-qubit gates that are represented by the Pauli matrices X, Y, and Z. They are used to perform rotations and flips on the qubit.
2. Hadamard gate: This is a single-qubit gate that transforms a qubit from the |0⟩ state to a superposition of |0⟩ and |1⟩.
3. Phase gate: This is a single-qubit gate that introduces a phase shift of π/2 to the |1⟩ state.
4. CNOT gate: This is a two-qubit gate that applies a NOT gate to the second qubit (target) only if the first qubit (control) is in the |1⟩ state.
5. SWAP gate: This is a two-qubit gate that exchanges the states of two qubits.
6. Toffoli gate: This is a three-qubit gate that applies a NOT gate to the third qubit (target) only if the first two qubits (controls) are both in the |1⟩ state.
There are many other types of quantum gates as well, each with its own unique properties and uses.