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The Fredkin gate (also CSWAP or CS gate), named after Edward Fredkin, is a 3-bit gate that performs a controlled swap. It is universal for classical computation. It has the useful property that the numbers of 0s and 1s are conserved throughout, which in the billiard ball model means the same number of balls are output as input.
[2] [3] [4] This set of gates is minimal in the sense that discarding any one gate results in the inability to implement some Clifford operations; removing the Hadamard gate disallows powers of / in the unitary matrix representation, removing the phase gate S disallows in the unitary matrix, and removing the CNOT gate reduces the set of ...
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 ...
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.
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 ...
def deutsch_jozsa_circuit (oracle, n_qubits): """ Assembles the full Deutsch-Jozsa quantum circuit. The circuit performs the following steps: 1. Start all 'input' qubits in |0>. 2. Start the 'output' qubit in |1>. 3. Apply Hadamard gates to all qubits. 4. Apply the oracle. 5. Apply Hadamard gates again to the input qubits. 6. Measure the input ...
The Hadamard transform H m is a 2 m × 2 m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2 m real numbers x n into 2 m real numbers X k.The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.
Jacques Salomon Hadamard ForMemRS [2] (French:; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations.