How to build a qubit (theoretically)?

[WAAAGH]

TL;DR Summary

My professor leaves me guidance on my dissertation and he instructs me to include the method of building a qubit theoretically.And I have no idea what it is at all.

And I was asked to include the deviation and the inherent process of the effective Hamiltonian of the charge qubit and the equation as well. And some of the derivation of the Hamiltonian as well. P.S The effective Hamiltonian formula is from the reference of :

https://www.researchgate.net/publication/323562386_Qubits_based_on_semiconductor_quantum_dots

 

[jambaugh]

Well, a Qubit is "simply" a two dimensional i.e. two "state" quantum system. You would have to describe what physical system you wish to theoretically use and how to implement all of the possible unitary transformations on that system in a controlled fashion. Since a lone qubit isn't worth much I would suppose you will need to also implement coherent transformations on a pair of such qubits, reading and writing their "quantum state" etc. Basically how to implement all the unitary transformations on a two qubit system with emphasis on those which correspond to classic logical operations, state exchanges and reading and writing.

 

[vanhees71]

I don't need to theoretically build a Qubit, because for the theorist it's enough to state: "consider an arbitrary two-level system". To the contrary the question is entirely experimental, and I don't know the details, how real-world quantum dots are really fabricated. There must be a plethora of literature about this since quantum dots are a hot topic in condensed-matter physics for several years (if not decades).

 

[Subluna]

You can employ another PhD student, hide him in a black-box with a coin (suitably rigged or not) and let him flip the coin. The output will be the same as output of some two-state quantum system, assuming the coin and the system state probabilities are the same.
That is how to create QuStudent emulating one QuBit. What the student is doing between your observations, you don't know.
To emulate a system of two QuBits is easy, just flip the coin two times. If you want qubits entanglement, just tell the student to flip once, observe the outcome and put the opposite outcome on the second (entangled) qubit.

 

[PeterDonis]

That is how to create QuStudent emulating one QuBit.

No, it isn't. What you describe realizes a classical bit, not a qubit. You cannot model quantum interference phenomena this way.

 

[Subluna]

No, it isn't. What you describe realizes a classical bit, not a qubit. You cannot model quantum interference phenomena this way.

How to model just one qubit?
ok, this QuStudent is not enough for performing real quantum computation,
but I assume that reading a qubit we get 0 or 1, with corresponding probabilities. Is it true?
Doing this N times (or using N students simultaneously) we get roughly N1 state 0 and N2 state 1, N1+N2 =N ?

 

[PeterDonis]

How to model just one qubit?

With the complex Hilbert space $\mathbb{C}^2$ and the appropriate operators on it.

I assume that reading a qubit we get 0 or 1, with corresponding probabilities.

Yes. But "reading a qubit" is not the only thing you can do with a qubit.

Doing this N times (or using N students simultaneously) we get roughly N1 state 0 and N2 state 1, N1+N2 =N ?

Not using N students simultaneously, because the task was to build just one qubit, not N of them.

Reading the one qubit N times, yes. But again, just reading the qubit N times is not the only thing you can do. Your model has to include all the things you can do with the qubit, not just reading it.

 

[WAAAGH]

Actually , my professor just clarified that he wants me to express the time evolution of the Hamiltonian under the Schrodinger equation (time - depended) and how to simulate it using analytical tool such as Matlab

 

[PeterDonis]

the time evolution of the Hamiltonian under the Schrodinger equation (time - depended)

The Schrodinger Equation doesn't determine the time evolution of the Hamiltonian. It determines the time evolution of the wave function. The Hamiltonian's time evolution, if any, has to be known in advance and plugged into the equation.