Quantum Computers — Part 3
The more you study about quantum computers, the more you want to delve into it. My recent discovery with the subject actually helped me understand the actual difference between a bit and a qubit. It also helped me understand a few important concepts like superposition, entanglement, and measurement. Let me help you sail through these below.
Quantum computing is the study of very small things like atoms, ions, photons, electrons, etc. These particles have a special property namely the spin. Qubits tend to be generated by one of the above-mentioned particles with the aforementioned property.
Qubits can be represented using the bra-ket notation: |0> or |1>, pronounced as ‘ket 0’ and ‘ket 1’ respectively.
As we already know, from my previous article that a qubit can have both values of 0 and 1 because of a superposition.
Why should we use spin as a qubit?
The simplest quantum bit in nature is called spin which you already know from schooldays atomic structure. Just like a compass needle, spin aligns with the magnetic field. The up-spin of a particle represents ket 1 and the down-spin represents ket 0. The figure below represents a particle in down-spin. When we irradiate this particle with an oscillating magnetic field whose frequency is proportional to the difference in the energy between the up-spin and the down-spin, the particle is forced to attain an up-spin. Thus, to flip the state of a spin we need an oscillating magnetic field that has the previously mentioned property.
The particle, after obtaining an up-spin is as shown below:
Thus, the two states of a qubit can be very well defined using the spin of a microscopic particle. The difference between a spin and the magnetic needle of a compass is evident when we observe the spin and what happens when two spins are close together.
The above situations cause two phenomena to take place:
- Quantum Measurement
- Quantum Entanglement
Each of which is described in depth below.
Quantum Measurement
It is being told that a qubit can exist in both the 0 and 1 states at the same time and which is possible because of the superposition of the up-spin and the down-spin.
Following is a spin in state 0:
The superposition of a particle in 0 and 1 states is shown below:
This was about the superposition of spins of a single particle.
But, when we want to check the spin it can only either be in state 0 or in state 1 but not in both simultaneously. This concept that causes the state of the spin to collapse to either 0 or 1 is called quantum measurement. Quantum Mechanics imposes that we can only find the spin state in either up or down position. Thus the act of measuring the quantum state destroys the superposition of the qubit and we are not able to access all of the coefficients of the superposition states all at once. The alpha, beta, gamma, and delta symbols below represent such coefficients. These coefficients determine the probability(given by the square of the coefficients) of finding the qubits in of the states(00, 01, 10 or 11).
Thus, N qubits need 2^N coefficients to represent the superposition of the qubits. Thus, the search space for the solution represented by a quantum system is exponential and thus it can help represent and solve some very complex problems.
This can also be understood from Schrodinger’s cat experiment. When we put a cat in a bunker with some explosive and close it, then there is a 50 percent chance that the explosive will explode and a 50 percent chance that it won’t until we look inside the bunker. But when we do look inside the bunker, then the cat will be either dead or alive. Thus, our curiosity killed the cat or that until we looked in the bunker, the cat was both dead and alive and was in a superposition but our curiosity to look inside the bunker will cause on of the events to occur and thus the reality collapses into one of the states.
Quantum Entanglement
What happens when more than one spins are there?
In the presence of another spin, there is a tiny magnetic field due to the spin of the other spin too. Thus, this changes the energy of the other spin and is thus dependent on the spin of in its vicinity, if any.
Assume that spin A was in 0 state initially. We then apply a magnetic field to cause a superposition of 0 and 1 states for spin A which causes it to face right(similar to vector addition) as shown below. When the spin A is set into a superposition of 0 and 1, then it can be said that it is both in state 0 and state 1. Now a spin B is introduced in the scene which has a 0 state and faces downwards as shown below. It’s energy changes as explained above. Now when we apply an oscillating magnetic field proportional to the energy difference between 0 and 1 states, when spin A was in 0 state, then spin B both flips to 1 and does not flip to 1.
Thus, the resulting state is a superposition of both 01 (pronounced as zero one) and 10.
This is a really special idea, wherein we do not know where the spins are pointing but we do know that they exist in opposite directions. Also, it is very difficult to simulate this in classical code because we cannot have two bits such that they do not have any values but at the same time have opposite values. This can perfectly be done using quantum computing using this concept of entanglement wherein two spins when in the picture shown above are separated and the spin of A is measured then we can dependently conclude that spin B will be of an opposite spin without even looking at spin B no matter how far apart spin A and spin B are in the universe. This is what Einstein called his spooky action at a distance.
These entangled states are the key to exploiting quantum information as these entangled states grow exponentially with the number of qubits and this is very intrinsic to the quantum realm. But these entangled states are really delicate and affected by the unwanted interference from the outside world and thus it requires a lot of effort in building a quantum computer.
Next
In the next article, we will dive deep into the various logic gates needed to construct a quantum logic circuit.
Let me know in the comments if I missed something.Feel free to give a feedback on the article as well if you found it informative.
