The title of this post is something very serious, even if it may appear crazy. It is indeed not that weird to discuss quantum computing and cats within the same post. This is what I will (try to) prove here.
[image credits: Wikimedia (public domain)]
This post follows an interesting discussion we had the other day on the steemstem chat about the famous Schrödinger’s cat thought experiment.
Some mentioned that this ‘experiment’ was a paradox, something that I strongly disagree with.
With this post, I will extend my reasoning a little bit and provide more details, which will naturally bring us to the notion of quantum decoherence.
And for those interested by a ‘TL;DR’ (for once, I can start with the summary), quantum decoherence is what must be fought at all costs for making quantum computing available in everyday’s life.
Now you got the connection :)
As usual, a stupid stuff is hidden in this post… ;)
One of the key principles behind quantum mechanics is the superposition principle. In a couple of words, this principle states that a quantum state can be seen as a superposition of different more basic components.
[image credits: Belsazar (CC BY-SA 3.0)]
A simple example can be seen in the qubit. After all, I will briefly discuss quantum computing in this post so that we could start with a naive version of the qubit as an example.
For a classical computer, a bit has to be either 0 or 1. In term of quantum state, it is correspondingly either in a
| 0 > state or in a
| 1 > state.
A qubit consists in contrast in a combination of these two basic ingredients. It has hence at the same time a non-vanishing 1 and a non-vanishing 0 component.
The corresponding quantum state could be written as
α |0> + β |1>, with the α and β coefficients being potentially different. A qubit could hence be more 0-dominated or 1-dominated according to the values of our two α and β coefficients.
At our macroscopic scale, there is nothing equivalent to such a superposition principle, and it is fair to say that it hurts our naive, classical, vision of nature. This weirdness was highlighted by Schrödinger who thought about an imaginary experiment aiming to contest the validity of quantum superposition.
The idea was to design a shocking and non-reasonable situation, implying that the only reasonable conclusion was to reject quantum superpotions. Of course, Schrödinger failed ;)
THE SCHRÖDINGER’S CAT EXPERIMENT
The heart of the Schrödinger’s cat experiment is to mix a macroscopic system (a cat) with a microscopic system (an atomic nucleus). I insist: this is a thought experiment. No cat has therefore ever been hurt by quantum mechanics.
[image credits: Robert Couse-Baker (CC BY 2.0)]
We imagine that a cat is sealed inside an opaque box together with a vial of poison whose opening would kill the animal.
The experiment starts with a vial that is closed and a cat that is alive.
The box however includes a mechanism that allows the vial to open, the mechanism being piloted by the decay of an atomic nucleus.
This is where nuclear physics enters into the game. It tells us that our nucleus has a given probability to decay which increases with time.
Therefore, the nucleus can decay at any time, but the decay will always happen after a sufficiently long time. And at that exact moment… the vial opens and wooof the cat…
The nucleus has to obey to quantum mechanics, as it is a microscopic object. We can thus write a quantum state for it. This state is very similar to the qubit quantum state introduced above, but after replacing the 0’s and 1’s by a decayed and a non-decayed status.
The quantum state of the nucleus reads thus
α(t) |decayed> + β(t) |non-decayed>, with the α and β coefficients depending on the time t. Nuclear physics then tells us that after some time, α(t) is close to 1 and β(t) is close to 0.
TOWARDS A QUANTUM CAT
And here comes Schrödinger’s provocation: including a macroscopic object (the cat) in the quantum state,
α(t) |decayed & dead> + β(t) |non-decayed & alive> to go back to the above notations.
[image credits: dingler1109 (CC BY 2.0)]
In other words, Schrödinger decided to apply the rules of the quantum world to the cat whose destiny depends on the vial, and thus on the nucleus.
If the nucleus has decayed, then the cat is dead. However, if the nucleus is intact, then the cat is alive.
And here is the funny and weird situation: the interpretation.
According to quantum mechanics, the cat is a zombie as neither alive nor dead as long as no one opens the box to check.
That is the crucial point. Before a measurement aiming to check the health of the cat, quantum mechanics tells us that the cat is partly alive and partly dead. After such a measurement, of course the cat is either dead or alive…
Quantum mechanics predict that once a measurement is undertaken, either the nucleus has decayed and the cat is dead, or it hasn’t and the ca tis alive. The zombie state of the cat is not observable.
SUMMARY: ALLEVIATING A NO-PARADOX AND QUANTUM COMPUTING
There is no paradox of the Schrödinger cat. Even if you can read the opposite in many places on the web (please do not trust anything you find on the Internet).
What one has here is a paradoxal interpretation of a state that is not observable in an experiment that is useless as no one will challenge what will be found at the time of the measurements.
Our macroscopic common sense tells us that the quantum state above-introduced, that we wrote
α(t) |decayed & dead> + β(t) |non-decayed & alive>, is non-realistic as zombie cats do not exist. This was also the point of Schrödinger, which thus challenges quantum superposition.
In fact, writing a quantum state for a cat has no sense at all, no matter it is dead, alive or zombie. The reason is that a cat has continuous exchanges with its environment, as most macroscopic systems. The ‘cat system’ is thus not an isolated system.
This means that in no time, its description through a quantum state is not valid anymore. This is what is called quantum decoherence. Decoherence appears at a pace proportional to the number of involved particles, and it has been observed and studied for instance in experiments with simplified pseudo-Schrödinger’s cats made of light.
For a cat, decoherence would be so fast that there is no way to observe any quantum effect. It is also the technological barrier to bypass for quantum computing.
Decoherence can indeed reduce a qubit to a classical bit, and makes us lose all the advantages of quantum computing. This is why quantum computers do not have at the moment a large number of qubits. It is damned hard to protect them from decoherence on a technological standpoint.
I hope that I have now convinced about this connection between cats and quantum computers :)
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