Intuition behind Superconductivity and Qubit Measurement and Control

In last blog I promised that we will talk about how to use quantum computer to write some programmes. But I think there is one last piece of puzzle is missing before we will get there.

So what is that ?let’s see ,if you would have followed all my previous blogs ,then I am hoping you must have good understanding about making of superconducting qubits which is essential to lay down the right foundation in your journey of quantum computing

 So what is missing why can’t we jump directly to programming? because programming is useful only when we know how to control these qubits and how to read these bits, but till now we understood only how to make them .

That is why I thought before starting our qubit programming voyage Let us take one more stop to talk about controlling and measurement of qubits.

So in this blog we will understand how to read qubits and how to control them ,similar to what we do with bits ,we can read the bits that whether they are zero or one ,as well as we can set them 0 or 1 by controlling the current .

 In last blog we talked about how coupling of current in Josephson junction and how wave function of this coupled current measured from outside in terms of magnetic flux using squid.

In this blog we will talk about how to interpret qubit wavefunction using magnetic flux and how to control this wavefunction and utilize it in writing important information on qubits.

Let us recall first what is a wave function

Wave Function defines the probability of finding an electron in certain position, so what are the possible positions for an electron. Let us understand Bohr model of hydrogen atom for this

“Bohr model of the atom was proposed by Neil Bohr in 1915. It came into existence with the modification of Rutherford’s model of an atom. Rutherford’s model introduced the nuclear model of an atom, in which he explained that a nucleus (positively charged) is surrounded by negatively charged electrons.

Bohr modified this atomic structure model by explaining that electrons move in fixed orbitals (shells) and not anywhere in between and he also explained that each orbit (shell) has a fixed energy level. “

Source: https://byjus.com/chemistry/bohrs-model/

So basically, what we are saying with this, that we want to understand in which shell electrons are present, because electrons wave function will be different on basis of their shell. As we know, our magnetic flux and current is correlated with our wave function, so basically, we should get different values of magnetic flux and current as per the shell of electrons.

So, let us understand can we correctly represent the electron wave function using the magnetic flux and current.

So as mentioned earlier electron can present in different energy levels around nucleus and these energy level represents different states of electrons or wave function of electron ,so if electron is at energy level 1 then its wave function will be different from energy level2 .So with this hypothesis of Bohr only one electron should be allowed in one energy shell ,but when scientist observed more complex atoms then Hydrogen, then they found that multiple electrons are possible in one energy level .

But as per Pauli’s rule ,it’s not possible, in one state only one electron is possible, multiple photons are possible in one state, but not multiple electrons.

After Further extensive experiments, scientist found out that inside one shell there are subshells possible, because although electron can’t move from one shell to another until it didn’t get energy required to jump from one shell to another, but it doesn’t means that it stays still ,it keep on moving in this shell in different orbits ,that’s why different subshells are possible in one shell and multiple electrons are possible in one shell . Wavefunction of these electrons will be defined by their orbits and movement of electrons in these orbits.  

Wavefunction of electron is defined by 4 quantum numbers

  • Principal quantum number (n) – This value indicates the shell/energy level of electron
  • Azimuthal quantum number (ℓ) – This value indicates the orbit number in which electron is rotating inside a shell.
  • Magnetic quantum number (mℓ)- This value indicates the angular momentum of electron in this orbit.
  • Spin quantum number (s)-This value indicates the spin of electron in its orbit. Two possible values of orbits are +1 and -1.

Movement of electrons in these orbits looks like below

Source- Electron Movement in different energy shells

Means all electrons in one shell will have same energy value but different wave functions, but from outside we can measure only energy ,nothing else ,so that’s why these multiple wave functions of electron are call degenerate energy levels

Source: Wikipedia Degenerate Energy Levels

Ground state is always non degenerate ,means only one electron present in this shell ,but in higher shell multiple electrons are present but with different wave functions ,so basically we can’t measure wave functions of these electrons correctly.

That’s why Cooper pairs are important ,as in cooper pair phenomenon ,electrons create a bond and all electrons present at same energy level are actually bound together and they have one single wave function because their movement stopped ,so now these copper pairs can move from shell to another but don’t move in one shell ,so now we have one wave function per shell . So now magnetic flux and current can represent the wave function of copper pairs correctly.

I think now you understood why superconductivity is important ,as superconductivity generates the phenomenon of one wave function per energy level ,which can be measured at macroscopic level

So by measuring the energy level ,we can measure the state of cooper pairs .

Now second question comes related to controlling of these cooper pairs ,We not only want to read the wavefunction of copper pairs correctly ,we want to control the movements of copper pairs as well from one energy level to another, then only we will be able to create successful qubit .

That problem is not even solved by copper pair’s ,why? because gap  between each energy shell is equal ,means if we want to move cooper pairs from shell K to shell M  or shell M to shell N ,we need to provide same amount of energy to copper pairs.

So what is problem with that ,so let’s say we have multi-qubit system, one qubit will be represented by bond of copper pairs which are present in same energy level .

Now let’s say some cooper pairs are present in shell K ,while others are present in shell M ,now we want to move cooper pairs present in shell K to shell M (its similar to changing bit 0 to bit 1) ,but now because same energy is required to move from energy level (shell)M to N as well ,so we can not guarantee that with this energy cooper pairs present at energy level K only will move ,copper pairs present at energy level M can also move to energy level N ,so with equal energy gaping it’s not possible to write information on qubits.

Now Josephson junction solves this problem for us ,so because of coupling of current ,energy gaping between two energy levels becomes different ,means if you want to move from energy level K to M then you need to provide different energy and for energy level M-N different energy is required .

Now we can on and off the qubit or write information on qubit ,I hope you all have better understanding about qubit measurement and control.

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