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The Hadamard transform is used extensively in quantum computing. The 2 × 2 Hadamard transform is the quantum logic gate known as the Hadamard gate, and the application of a Hadamard gate to each qubit of an -qubit register in parallel is equivalent to the Hadamard transform .
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.
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.
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.
In quantum computation, the Hadamard test is a method used to create a random variable whose expected value is the expected real part | | , where | is a quantum state and is a unitary gate acting on the space of | . [1]
A CNOT gate may appear to only act the control on the target, but surrounding it with Hadamard gates reveals it also acts the target on the control. A CNOT appears asymmetric, but can be transformed into a symmetric operation by Hadamard gates. Symmetric operations don't distinguish target and control, resulting in effects like phase kickback.
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):
Arbitrary Clifford group element can be generated as a circuit with no more than (/ ()) gates. [6] [7] Here, reference [6] reports an 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C-, where H, C, and P stand for computational stages using Hadamard, CNOT, and Phase gates, respectively, and reference [7] shows that the CNOT stage can be implemented using (/ ()) gates (stages -H- and -P ...