Supervised learning of random quantum circuits via scalable neural networks

TL;DR

This paper demonstrates that scalable convolutional neural networks can accurately predict quantum circuit outputs, outperforming small quantum computers in some cases, and are resilient to noise, aiding quantum computer development.

Contribution

It introduces scalable CNN architectures for supervised learning of quantum circuit outputs, enabling extrapolation to larger circuits and robustness against noise.

Findings

CNNs outperform small quantum computers in prediction accuracy

Scalable CNNs can extrapolate to larger circuits beyond training set

CNNs maintain accuracy even with limited measurement data

Abstract

Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are represented via an appropriately designed one-hot encoding of the constituent gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform the quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements.