Practical Guide to Quantum Computing: CX Gate (CNOT, Controlled-NOT Gate)

Mikhail Pavlov

Published Mar 4, 2026• 0 citations

Abstract

The CX gate (CNOT, controlled-NOT gate) is a fundamental two-qubit quantum gate that flips the state of the target qubit conditional on the state of the control qubit. Specifically, if the control qubit is in the ∣1⟩|1\rangle∣1⟩ state, the CX gate inverts the target qubit; if the control qubit is in ∣0⟩|0\rangle∣0⟩, the target qubit remains unchanged. The CX gate is a cornerstone of quantum computing, enabling the creation of entanglement between qubits, which is essential for quantum algorithms and quantum error correction. It serves as a building block for more complex quantum circuits, such as quantum teleportation, superdense coding, and multi-qubit gates. Mastery of the CX gate is critical for designing and implementing practical quantum computations on platforms like IBM Q.

DOI: 10.5281/zenodo.18862788

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