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Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices. 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.
In gate-based quantum computing, various sets of quantum logic gates are commonly used to express quantum operations. The following tables list several unitary quantum logic gates, together with their common name, how they are represented, and some of their properties.
The classical analog of the CNOT gate is a reversible XOR gate. How the CNOT gate can be used (with Hadamard gates) in a computation.. 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.
Other examples of quantum logic gates derived from classical ones are the Toffoli gate and the Fredkin gate. However, the Hilbert-space structure of the qubits permits many quantum gates that are not induced by classical ones. For example, a relative phase shift is a 1 qubit gate given by multiplication by the phase shift operator:
More recent motivation comes from quantum computing. In quantum mechanics the quantum state can evolve in two ways: by Schrödinger's equation (unitary transformations), or by their collapse. Logic operations for quantum computers, of which the Toffoli gate is an example, are unitary transformations and therefore evolve reversibly. [2]
Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations. A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system.
The Clifford gates do not form a universal set of quantum gates as some gates outside the Clifford group cannot be arbitrarily approximated with a finite set of operations. An example is the phase shift gate (historically known as the π / 8 {\displaystyle \pi /8} gate):
Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit.
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