Quantum Darwinism To Artificial Neural Network
By: Siddharth Saraf
Tags: Artificial Intelligence, Quantum Computing, Deep Learning, Quantum Mechanics, Human Brain

In the quantum world, things are routinely in a quantum superposition state.

The famous thought experiment is Schrodinger's cat in which the cat is both alive and dead until a portion of deadly poison that is released on the radioactive decay of an atom.

Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states-simultaneously decayed and not decayed.

That means is the wavefunction of the cat is also in a state of superposition of dead and alive? The answer is yes, even though it seems crazy and impossible.

Superposition is the basis of quantum mechanics. If there are two valid states then the sum of those two states is also a valid state.

It is not that this happens in the Quantum world and we can ignore this. Because, the quantum world is nowhere in the alien universe but within ourselves, at the most basic level of matter building.

That means whatever we see, touch or feel is the product of the interaction of the quantum objects and their interactions.

The process of disappearance of this crazy behavior in the classical world or the macro world is possible due to another process called decoherence- to observe a superposition there should a knowable phase relation between two superposed states.

This is a partial answer and this doesn’t explain why only certain states are visible to the macro world(our world).

The answer is obtained by taking another property called Quantum Entanglement.

Entanglement is so powerful and important that the properties that we think of as fundamental like the arrangments of atoms that dictate the cat (or any living/nonliving object) is alive or dead aren’t the properties of the atoms!

Rather, the information that defines the classical properties originated from the complex network of entanglement between those individual quantum systems and their environments.

For people who are new to Quantum Systems, let’s start with the spin direction of an electron. This Quantum spin has axis either in a vertical direction or horizontal direction.

As mentioned above due to superposition property the axis direction is in both vertical and horizontal directions simultaneously. Now to measure the spin direction, we have to choose the measurement direction i.e. either vertically or horizontally. If we measure vertically we find that the axis is in a vertical direction (up or down) and if we measure horizontally, we find the axis in the horizontal direction( left or right).

A particle in Quantum Superposition

Weirdly if we first measure the spin vertically, we note the direction and then measure the spin in the horizontal direction we still see the spin in horizontal direction NOT in vertical as found earlier. This shows the output of the quantum states depends on the measurement-basis; every time.

Now how this state is traversed to the classical world, the answer is quantum entanglement. It was earlier proposed by Einstien, Podolsky, and Rosen and was called “Spooky action-at-a-distance”.

This “bond” or “spooky action-at-a-distance” is so fast that if two objects are entangled and places at opposite ends of the Universe, they can communicate instantly.

The appearance of the quantum object to us occurs when the wavefunction of the quantum object collapses. For decades scientists wanted to observe the “real” state of quantum objects but they failed since the sere act of measurement destroys the original quantum states.

For searching the reason for this one scientist named Wojciech Zurek theorized an idea called “Quantum Darwinism”. It is built on the idea of the ‘survival of fittest’ principle from Charles Darwin’s Theory of evolution.

When a measurement device is kept near a quantum system to measure the quantum property, the device is entangled with the quantum system and becomes part of the entanglement network. Hence if a person tries to record the measurement from the device, he/she collapses the wavefunction of the entire Quantum System which now includes the measuring device.

As more and more particles/objects join the entanglement web, information about quantum states get spread among all the entangled objects. According to Zurek’s theory, eventually, the entanglement cascade reaches the surrounding environment and is no longer bounded resulting in most of the quantum information trapped and unrecovered.

But there is certain information that is not mixed and is reflected in the surrounding measuring environment. These are called ‘Pointer States’, which are copied and spread until the measuring device.

Through EINSELECTION- Enviromnatally Induced Superselection, the basis states like the direction of measurement become the “fit” state which survives and replicates throughout the Entanglement network.

In other quantum systems, like this, the relative location of interacting particles is robustly shared and propagated through the Entanglement network. Hence, even though the individual particles do not have well-defined states(e.g. locations) but the entanglement network has a collective consensus about those locations.

This is the reason the bigger objects like cats, dogs or humans have a well-defined position since their internal Quantum Entanglement Network has well-defined knowledge about the relative positions of the inherent particles.

Learning about this propagating pointer states and Quantum Entanglement one thing came to my mind and that is working of Neural Network in Deep Learning in computers.

See, because the neural network is also a connected network of neurons, it’s logical to compare it with Quantum Entanglement Network.

The Input neurons in the Input Layer is like the initial quantum particles and the intermediate hidden layers having hidden neurons are like entangled particles. The output neurons in the output layer are like measuring device. The connection from one neuron in one layer to another neuron in another layer can be considered as Entanglement. Finally, the wights of the connections between layers are similar to pointer states as ideated by Wojciech.

Loss Function the value of which to be minimized

The Neural Network learns the ideal set of weights to represent the loss function and to minimize the loss. It isn’t exactly trivial for us to work out the weights just by inspection alone and hence the network finds its proper wight by itself. The operations done by each neuron are simple :

Apart from the input, output, biases, layers, and neurons, it needs one more important entity called Activation Function. Activation functions are important for an Artificial Neural Network to learn and make sense of complicated operations happening in the network and Non-linear complex functional mappings between the inputs and response variable. They introduce non-linear properties to our Network. Their main purpose is to convert an input signal of a node in an ANN to an output signal. That output signal now is used as an input in the next layer in the stack.

The most popular types of Activation functions are Sigmoid or Logistic, Tanh — Hyperbolic tangent and ReLu -Rectified linear units. Sigmoid function looks like:

Sigmoid Function and below is its graph

After training the neural network with test data the final output is delivered by the network with a certain degree of accuracy. The network is trained with many iterations which are called epochs.

What I tried to convey is the striking similarity between Quantum Entanglement and Artificial Neural Network and hence with the human brain. So, can in this way we prove that our brain is a Quantum Computer?

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