Quantum Similarity Testing with Convolutional Neural Networks
This addresses a crucial benchmarking need for near-term quantum computers and simulators, offering a novel solution for continuous-variable systems where previous methods failed.
The authors tackled the problem of testing similarity between unknown continuous-variable quantum states, which was previously unsolved for non-Gaussian states, by developing a convolutional neural network algorithm that works with limited and noisy data, achieving successful performance on noisy cat states and states from arbitrary selective number-dependent phase gates.
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.