Qubit is a two level system.

Qubit is a two-level system.

Qubit is a two-level system. Qubit control and measurement fundamentals

A year ago, before the pandemic, I started to learn the fundamentals of Quantum Computing. I needed to know the basics and understand the overall architecture of a superconducting universal gate-based quantum system. When researching qubit states, I learned the basic concept and math behind it and without this bit of knowledge, visualizing a qubit doing computation is a intellectually challenging hard concept. This post familiarizes you with qubit energy states, how to excite them to fall into each state, a basic understanding of superposition and required math, Plank constant, and Schroder equation. I did the drawing on paper and included with the post.

So let's look at the drawing. There is the Ground State. The other is quantize state.

So we'll call that N equals one on a horizontal axis for the Ground state. And there is the vertical axis here, and mark it as electron volts ( call it ev). What happens next is from the ground state, we go to the next quantized state, which is our first excited state, and we're going to call that N equals two. N=2

Now, if you put an electron in the ground state and then apply some electromagnetic energy central (sign wave) to the system, depending on the frequency of this waveform, because it's the photoelectric effect, we can make this electron jump up to the next quantize state.

And when we remove it, eventually all fall down and emit the same energy or the same frequency. And that frequency is equal to the energy of the excited state minus the energy of the ground state over Planck's constant. (6.62607004 × 10-34 m2 kg / s)

Imagine the electrons are tiny, little magnets, so they have poles and magnetic moments. So we can define that when it's in the ground state; North faces downwards and south-facing outwards, and then we can apply our magnetic energy -when we move it up, we find the next quantized state. -the Poles have swapped over. So now North is facing outwards, and South is facing downwards. And we call this magnetic moment the spin of an electron even though nothing actually spins. And when North is facing down, we call that the spin-down condition. And when North is messing up, we call that the spin-up state.

According to Schrodinger's equations, there is states in between, and there's a probability that this electron could be within a state between this energy level and the other energy level. So if we find an appropriate amount of electromagnetic energy at the system of the correct frequency, we can say with a certain amount of probability that our electron will be somewhere in between the excited state and the ground state. And also, the magnetic moment would be somewhere between the spin-up state and the spin down state, and it spins, or the magnetic moment that we actually measured in our quantum system.

See the picture above. We can visualize this on a unitary circle too, so if I draw a circle, we can say, we can find a measurement basis, and we'll say a spin down is equal to a vector on the horizontal axis -and we can say that is a quantum zero state.

And we know these are orthogonal; orthogonal means a right angle. So the spin-up condition is, orthogonal to the spin-down condition. And we can say that in bra-ket notation is, is our one state. And in vector notation, the x axis is one, and y axis is zero. For the other one, our x axis is zero and y axis is one. The superposition says there's a probability that there's going to be an electron, probably halfway in between. That is called superposition.

So superposition essentially means that the vector is a summation of these two vectors, right down the middle. And its Cartesian coordinates are one over root two comma one over root two. Now we have a complete quantum computing system, essentially, when we only had two states; spin up state and the spin down state. And we acquainted those to a logical One and logical Zero; we essentially had a register that represented a logical One and a logical Zero. We can now do gates and doc computations! -

That was a qubit two-level system explained in simple terms.

Next post : Superposition measurement and the NOT Gate -