Controlled NOT gate

In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-X gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states. Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. The gate is sometimes named after Richard Feynman who developed an early notation for quantum gate diagrams in 1986. The CNOT can be expressed in the Pauli basis as: Being both unitary and Hermitian, CNOT has the property and , and is involutory. The CNOT gate can be further decomposed as products of rotation operator gates and exactly one two qubit interaction gate, for example In general, any single qubit unitary gate can be expressed as , where H is a Hermitian matrix, and then the controlled U is . The CNOT gate is also used in classical reversible computing. The CNOT gate operates on a quantum register consisting of 2 qubits. The CNOT gate flips the second qubit (the target qubit) if and only if the first qubit (the control qubit) is . If are the only allowed input values for both qubits, then the TARGET output of the CNOT gate corresponds to the result of a classical XOR gate. Fixing CONTROL as , the TARGET output of the CNOT gate yields the result of a classical NOT gate. More generally, the inputs are allowed to be a linear superposition of . The CNOT gate transforms the quantum state: into: The action of the CNOT gate can be represented by the matrix (permutation matrix form): The first experimental realization of a CNOT gate was accomplished in 1995. Here, a single Beryllium ion in a trap was used. The two qubits were encoded into an optical state and into the vibrational state of the ion within the trap. At the time of the experiment, the reliability of the CNOT-operation was measured to be on the order of 90%.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related concepts (16)

Related courses (19)

Related lectures (195)

Reversible computing

Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from states to their successors must be one-to-one. Reversible computing is a form of unconventional computing. Due to the unitarity of quantum mechanics, quantum circuits are reversible, as long as they do not "collapse" the quantum states they operate on.

Quantum logic gate

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates.

Controlled NOT gate

CS-308: Quantum computation

The course introduces teh paradigm of quantum computation in an axiomatic way. We introduce the notion of quantum bit, gates, circuits and we treat the most important quantum algorithms. We also touch

PHYS-641: Quantum Computing

After introducing the foundations of classical and quantum information theory, and quantum measurement, the course will address the theory and practice of digital quantum computing, covering fundament

PHYS-454: Quantum optics and quantum information

This lecture describes advanced concepts and applications of quantum optics. It emphasizes the connection with ongoing research, and with the fast growing field of quantum technologies. The topics cov

Universal Quantum Computing Using Electronuclear Wavefunctions of Rare-Earth Ions

Gabriel Aeppli

We propose a scheme for universal quantum computing based on Kramers rare-earth ions. Their nuclear spins in the presence of a Zeeman-split electronic crystal field ground state act as "passive" qubit

AMER PHYSICAL SOC2021

Proof of Schmidt Theorem and Entropy Properties COM-309: Quantum information processing

Covers the proof of the Schmidt theorem and properties of von Neumann entropy, including dense coding and entanglement.

Quantum Measurement: General Description PHYS-758: Advanced Course on Quantum Communication

Explores the general description of quantum measurements, including post-measurement states and Kraus operators.

Quantum Computation Delegation

Explores fully classical qubits, blind quantum computing, and verifiability in quantum delegation protocols.