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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.
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 Hadamard test produces a random variable whose image is in {} and whose expected value is exactly | | . It is possible to modify the circuit to produce a random variable whose expected value is I m ψ | U | ψ {\displaystyle \mathrm {Im} \langle \psi |U|\psi \rangle } by applying an S † {\displaystyle S^{\dagger }} gate after the first ...
It is also based on the demonstrations that the probability of success of the quantum gates can be made close to one by using entangled states prepared non-deterministically and quantum teleportation with single-qubit operations [14] [15] Otherwise, without a high enough success rate of a single quantum gate unit, it may require an exponential ...
However, in quantum computing, operations have the ability to introduce phase changes to quantum states. This is the basis for complex interference patterns and quantum entanglement. When a controlled operation, such as a Controlled NOT (CNOT) gate , is applied to two qubits, the phase of the second (target) qubit is conditioned on the state of ...
The ZW-calculus was developed alongside the ZX-calculus, and can naturally describe the W-state and Fermionic quantum computing. [ 26 ] [ 27 ] It was the first graphical language which had a complete rule-set for an approximately universal set of linear maps between qubits, [ 8 ] and the early completeness results of the ZX-calculus use a ...
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.