Quantum Eyes

Turns out this simple neural network is able to achieve an 88% accuracy ! That’s pretty impressive, considering that it’s just a bunch of linear layers and activations. But let’s try something even better…

CNNs are actually able to achieve pretty insane results — 99.75% accuracy ! The reason why CNNs’ incredible power is due to it’s ability to look at the surrounding pixels and based off of that, extract features and information from that patch of pixels. Normal NNs can’t do that, so they’re a bit less powerful.

CNNs look like this:

The 3 main parts of a CNN are

Convolutional Layers : These are the layers which have kernels, they're really good at extracting features from the image and passing it on

Max Pooling Layers : These layers reduce the feature map (the size of the features), reduce the computational resources needed and prevents overfitting

Fully Connected Layers : They appear at the end of the CNN, they’re just linear layers which takes the results of the CNN as inputs and outputs the lable

That’s the architecture, but the really amazing part of a CNN are it’s kernels inside it’s convolutional layers! These kernels are only matrixes (basically a bunch of numbers sorted in a box), but they’re able to extract tons of features about the image.

By the first layer the kernels can start telling which images have verticle lines, horizontal lines and different colors. By layer 2 you can put those features together and form more comple shapes like corners or circles.

Layer 3 becomes even cooler! Repeating patterns, car wheels and even humans.

And as you stack your convolutions more and more you get more and more complex features — that’s insane becuase CNNs are able to extract those meta structures of the image.

By extracting those features you can put them in a neural network and classify your image! But as cool as that sounds, there are 2 Achilles heels:

1. When input dimensions increase exponentially, the time it takes to run the CNN also becomes exponential . An example of a problem like that would be when you’re modeling quantum systems to classical computers, the input space grows exponentially
2. As you increase the kernel size, the time it takes to run the CNN becomes exponential

But Quantum’s here to the rescue!

To tackle the first problem, we could just let qubits represent the quantum system! Introducing: Quantum Convolutional Neural Networks .

This is a neural network that literally replicates the whole CNN architecture. C onvolutional layers and max pooling are all translated to the quantum realm!

The architecture itself looks like this:

1.Convolutional layers : Instead of kernals, you have gates that are applied to the qubits adjacent to it

2.Pooling Layers : Where you just measure half of the qubits and kick out the rest

3.Fully Connected Layer: Just like the normal one

If you’re a super quantum nerd you might have noticed that this architechture might have some resemblence to a reverse MERA (Multi-scale Entanglement Renormalization Ansatz).

A normal MERA takes 1 qubit and then exponentially increases the number of qubits by introducing new qubits into the circuit.

But in the reverse MERA, we’re doing the

opposite by exponentially decreasing the number of qubits.

The bottleneck here is the range of possible qubits which the reversed MERA can reach.In other words, the QCNN might not be able to produce the labels. But we can overcome this by implementing Quantum Error Correction(QEC),the thing you see in the red box in the diagram.

This architecture works super well with problems that require a small input size,since our current quantum computers can’t hold that many qubits.But what if we wanted to use QCNN’s for image classifiction or other problems that need more input space?

A Quanvolutional Neural Network (QNN) is basically a CNN but with quanvolutional layers (much like how CNN’s have convolutioanl layers). A Quanvolutional layer acts and behaves just like a convolutional layer!

Much like a normal convolutional layer, we take a subset of the image, pass it through our kernal , and then it outputs a part of the new image. We do this over and over again until we reach the linear layer, which classify’s the image.

Since it acts so much like a normal Convolutional layer, you could literally use both a QNN and a CNN together in the same model!

• Noise Resistant : With Quantum Error Correction, along with it’s quantum nature, QNNs are resistant to constant noise. In current quatnum computers, there’s always a constant noise / error that occurs in quantum gates, but QNNs overcome it
• Better Results : In this paper , researchers use QNNs to diagnose Covid just from chest X-rays! They obtained a 98% accuracy, 2% better than standard CNNs!
• Faster Training Time : Classical CNNs have O(n²) time, where n is the kernal size. QNNs have O(log(n)) time! That’s an insane speedup!

• Many Executions Needed: Since we have to stamp the kernal all over the image, and do this to the potential of thousands of images, you’re going to have to run run the quantum circuit a lot. Current quantum computers aren’t able to handle that many executions
• Difficult to optimize : Inside QNNs there are things call encoding protocals . These protocals are very difficult to optimize. Researchers don’t know which protocols are good, useless or even counter productive!

These new Quantum Machine Learning algorithms are but a testament to what there is to come. Even though quantum computers are at it’s infancy, we have already seen these new QML algorithms which are already outperforming our old ones!

Many of our existing ML algorithms could be translated into QML algorithms, allowing them take avantage of new properties like entanglement, superpostion and insane parallel computing! It’s only a matter of time before these algorithms are changing the world!