Quantum Similarity Testing with Convolutional Neural Networks

TL;DR

This paper introduces a convolutional neural network-based method for comparing unknown continuous-variable quantum states, including non-Gaussian states, using limited and noisy measurement data, aiding in quantum device benchmarking.

Contribution

The authors develop a novel machine learning approach that enables similarity testing of complex quantum states, including non-Gaussian states, which was not possible with previous techniques.

Findings

Effective comparison of noisy cat states demonstrated.

Applicable to states from different experimental platforms.

Can test for Gaussian unitary equivalence.

Abstract

The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained offline with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, or with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.