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The rotation operators R x (θ), R y (θ), R z (θ), the phase shift gate P(φ) [c] and CNOT are commonly used to form a universal quantum gate set. [20] [d] The Clifford set {CNOT, H, S} + T gate. The Clifford set alone is not a universal quantum gate set, as it can be efficiently simulated classically according to the Gottesman–Knill theorem.
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 quantum logic gates are reversible unitary transformations on at least one qubit. Multiple qubits taken together are referred to as quantum registers. To define quantum gates, we first need to specify the quantum replacement of an n-bit datum. The quantized version of classical n-bit space {0,1} n is the Hilbert space
Care must be taken to end the gate at a time when all motional modes have returned to the origin in phase space, and so the gate time is defined by = = for each mode . For μ k t = 2 π {\displaystyle \mu _{k}t=2\pi } , the second term of M 2 ( t ) {\displaystyle M_{2}(t)} also vanishes, and so the time evolution operator becomes
a fixed but arbitrary list of static gates (quantum gates that do not depend on parameters, like the Hadamard gate.) G ′ {\displaystyle G'} a fixed but arbitrary list of parametric gates (gates that depend on a number of complex parameters like the phase shift gate that requires an angle parameter to be completely defined.)
A quantum circuit consists of simple quantum gates, each of which acts on some finite number of qubits. Quantum algorithms may also be stated in other models of quantum computation, such as the Hamiltonian oracle model. [7] Quantum algorithms can be categorized by the main techniques involved in the algorithm.
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.
For the purposes of quantum order-finding, we employ this strategy using the unitary defined by the action | = {| <, | <. The action of on states | with < is not crucial to the functioning of the algorithm, but needs to be included to ensure that the overall transformation is a well-defined quantum gate. Implementing the circuit for quantum ...