Quantum Neural Networks: What are they and why are they important?

Neural networks. That’s a common term in machine learning, and they’ve changed the game entirely. Now quantum is added to the field, and quantum mechanics complicate neural networks entirely.

A classical neural network is built on layers of nodes, weights, and activation functions. Typically a neural network works like this: data flows in, gets multiplied, transformed, and produces an output.

A Quantum Neural Network, or QNN, replaces that same structure discussed above but with quantum circuits. Instead of classical nodes, you have qubits (which I’ve touched on in all my previous articles). Instead of weight matrices, you have quantum gates (rotations applied to qubits). Now, with QNNs, data gets encoded into quantum states, processed through the circuit, and measured at the end.

“Measured.” Instead of producing an output, in quantum, measurement collapses qubit’s superposition into a definite 0 or 1 state (how a classical node works). The QNN’s output comes from the probability distribution of those measurements.

So why does this matter?

First, superposition. A qubit can exist as 0, 1, or any combination of both simultaneously. A QNN can explore a much larger solution because of this. Second, entanglement. Qubits can be correlated in ways that have no classical equivalent, and this allows the network to have dependencies which classical networks cannot mimic. Third, interference. Quantum circuits can be designed to amplify correct answers and cancel out wrong ones, which gives QNNs a lot more potential and could accelerate learning significantly.

What’s the issue then, why are QNNs not in place already?

QNNs are hard to train. There is something called the barren plateau problem. When you train a neural network, you adjust parameters based on gradient descent: essentially, you are saying how much does changing the parameter improve the output? In QNNs, as the circuit gets bigger and bigger, those gradients get smaller and smaller, to the point where they become indistinguishable from zero. The network can’t learn because everything becomes so spread out and it doesn’t know which direction to move towards.

In spite of this, progress is happening. Variational Quantum Eigensolvers and QAOA have shown that hybrid classical-quantum approaches can take advantage of today’s hardware.

However, it is important to mention that QNNs aren’t replacing classical deep learning models tomorrow or within a year’s time, but that it represents a path towards a new approach to computation. The future is closer than most people think.

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