kaksiqubitportteja

Kaksiqubitportteja, also known as two-qubit gates, are fundamental operations in quantum computing used to manipulate the state of two qubits simultaneously. These gates are essential for creating entanglement, a phenomenon where the state of one qubit becomes dependent on the state of another, even when separated by distance. The most well-known two-qubit gate is the Controlled-NOT (CNOT) gate, which flips the state of the target qubit if the control qubit is in the state |1⟩.

Two-qubit gates can be represented using matrices in a similar manner to single-qubit gates. However, they operate on a larger Hilbert space, as they need to account for the combined state of two qubits. For example, the CNOT gate can be represented by the following matrix:

| 1 0 0 0 |

| 0 1 0 0 |

| 0 0 0 1 |

| 0 0 1 0 |

This matrix acts on the four basis states of two qubits: |00⟩, |01⟩, |10⟩, and |11⟩. The CNOT gate leaves the states |00⟩ and |01⟩ unchanged, while it flips the states |10⟩ and |11⟩ to |11⟩ and |10⟩, respectively.

Other important two-qubit gates include the SWAP gate, which exchanges the states of two qubits, and the controlled-Z (CZ) gate, which applies a phase flip to the target qubit if the control qubit is in the state |1⟩. These gates, along with the CNOT gate, form a universal set for quantum computation, meaning that any quantum circuit can be constructed using only these gates and single-qubit gates.

Two-qubit gates are typically implemented using physical interactions between qubits, such as the exchange of photons or the coupling of superconducting circuits. The fidelity of these gates is a critical metric for quantum computers, as it determines the accuracy of quantum operations and, consequently, the overall performance of the device.