Generating 3 qubit quantum circuits with neural networks

TL;DR

This paper introduces a neural network-based method for compiling three-qubit quantum circuits by decomposing unitaries into simpler components, leveraging geodesic-based training data to improve efficiency and uniqueness.

Contribution

It presents a novel neural network approach for quantum circuit compilation that utilizes geodesic-based data to enhance decomposition accuracy and circuit generation.

Findings

Neural networks achieve low validation loss after short training.

Method produces coefficients close to true values, validating the approach.

Effective for three-qubit systems, with potential for scaling.

Abstract

A new method for compiling quantum algorithms is proposed and tested for a three qubit system. The proposed method is to decompose a a unitary matrix U, into a product of simpler U j via a neural network. These U j can then be decomposed into product of known quantum gates. Key to the effectiveness of this approach is the restriction of the set of training data generated to paths which approximate minimal normal subRiemannian geodesics, as this removes unnecessary redundancy and ensures the products are unique. The two neural networks are shown to work effectively, each individually returning low loss values on validation data after relatively short training periods. The two networks are able to return coefficients that are sufficiently close to the true coefficient values to validate this method as an approach for generating quantum circuits. There is scope for more work in scaling this approach to larger quantum systems.

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