a well-known gate in quantum computing that achieves this

The Hadamard Gate is a well-known gate in quantum computing that achieves this.

The quantum gates used in the circuit

The quantum gates used in the circuit are the Hadamard gate and the controlled phase gate , here in terms of with the primitive -th root of unity.

the quantum Fourier transform

The modular exponentiation is the single controlled-NOT, and the quantum Fourier transform is a Hadamard gate.

a qubit

The Hadamard gate puts a qubit into a superposition of states, and the CNOT gate creates entanglement between two qubits.

into a superposition of states

The Hadamard gate puts a qubit into a superposition of states, and the CNOT gate creates entanglement between two qubits.

a rotation that swaps the x-axis and z-axis of a given qubit

A Hadamard gate is a rotation that swaps the x-axis and z-axis of a given qubit.

Another standard gate

Another standard gate is the Hadamard gate, which can be defined as follows.

the combination of two rotations, about the Z-axis followed by about the Y-axis

Equivalently, The Hadamard gate is the combination of two rotations, about the Z-axis followed by about the Y-axis.

a unitary operation that transforms a qubit from the computational basis state |0

The Hadamard gate is a unitary operation that transforms a qubit from the computational basis state |0

a 1-qubit rotation, mapping the qubit-basis states and to two superposition states with equal weight of the computational basis states and

The Hadamard gate is a 1-qubit rotation, mapping the qubit-basis states and to two superposition states with equal weight of the computational basis states and .

nothing more that the quantum fourier transform over the simplest of all groups

The Hadamard gate is nothing more that the quantum fourier transform over the simplest of all groups, the cyclic group with two elements, Z_2.

a universal gate set for quantum computing

The Toffoli gate with the Hadamard gate is a universal gate set for quantum computing.

the simplest method for generating a random bit in a qubit

The Hadamard gate is the simplest method for generating a random bit in a qubit.

a rotation of about the axis at the Bloch sphere

The Hadamard gate represents a rotation of about the axis at the Bloch sphere.

some of the elementary quantum gates that are identified in the stock market structure

Hadamard gate, Pauli gates or controlled-Z gate are some of the elementary quantum gates that are identified in the stock market structure.