What does the Bloch sphere represent?

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space.

How do you read a Bloch sphere?

The Bloch Sphere is is a generalisation of the representation of a complex number z with |z|2 = 1 as a point on the unit circle in the complex plane. and x2 + y2 = 1 is the equation of a circle of radius one, centered on the origin. Notice that the constraint |z|2 = 1 has left just one degree of freedom.

Which of the following operators is used to perform a rotation about the Z axis on a qubit state on the Bloch sphere?

Rx,y
exercise: convince yourself that the operators Rx,y,z do perform rotations on the qubit state written in the Bloch sphere representation.

How do I rotate in qubit?

The states of the qubit can be transformed by rotating it around axis x, y, and z. The operation used to rotate a single qubit around X-axis. The Rx gate implements a rotation of π i.e 180 degrees around the X-axis of the block sphere. The X gate is also called the NOT gate.

What is the number of qubits in the Clifford simulator?

Our C++ implementation of the simulator performs approximately 5 × 106 Clifford gates per second for n = 64 qubits on a laptop computer.

Is quantum Fourier transform unitary?

We have seen that the quantum Fourier transform is a unitary operator. Therefore, by our earlier results, there is a quantum circuit which implements it. However, there is no guarantee that this circuit will be efficient! A general unitary requires a circuit with a number of gates exponential in the number of bits.

What is a Bloch ball in quantum mechanics?

The density operator describing the mixed-state of a 2-level quantum system (qubit) corresponds to a point inside the Bloch sphere with the following coordinates: are the coordinates of the individual states (on the surface of Bloch sphere). The set of all points on and inside the Bloch sphere is known as the Bloch ball.

What is the Bloch sphere?

Understanding the Bloch sphere. It is usually said that the points on the surface of the Bloch sphere represent the pure states of a single 2-level quantum system. A pure state being of the form: |ψ⟩ = a|0⟩+b|1⟩ And typically the north and south poles of this sphere correspond to the |0⟩ and |1⟩ states.

How does the Bloch sphere parametrize mixed states?

The Bloch sphere parametrizes not only pure states but mixed states for 2-level systems. The density operator describing the mixed-state of a 2-level quantum system (qubit) corresponds to a point inside the Bloch sphere with the following coordinates: are the coordinates of the individual states (on the surface of Bloch sphere).

What is the Bloch vector in physics?

is called the Bloch vector. It is this vector that indicates the point within the sphere that corresponds to a given mixed state. Specifically, as a basic feature of the Pauli vector, the eigenvalues of ρ are