Giulio Chiribella

Ning Gao, Dantong Li, Anchit Mishra et al.

The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED provides a metric on the space of von Neumann measurements, and can be efficiently estimated by letting the measurement processes act in an indefinite order, using a setup known as the quantum switch, which also allows one to quantify the noncommutativity of arbitrary quantum processes. Thanks to these features, the MED can be used in quantum machine learning tasks. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise can be used to identify groups of observers that share approximately the same measurement context.

Ya-Dong Wu, Yan Zhu, Ge Bai et al.

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.

Ya-Dong Wu, Yan Zhu, Yuexuan Wang et al.

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

Manwen Liao, Yan Zhu, Giulio Chiribella et al.

Quantum error mitigation, a data processing technique for recovering the statistics of target processes from their noisy version, is a crucial task for near-term quantum technologies. Most existing methods require prior knowledge of the noise model or the noise parameters. Deep neural networks have a potential to lift this requirement, but current models require training data produced by ideal processes in the absence of noise. Here we build a neural model that achieves quantum error mitigation without any prior knowledge of the noise and without training on noise-free data. To achieve this feature, we introduce a quantum augmentation technique for error mitigation. Our approach applies to quantum circuits and to the dynamics of many-body and continuous-variable quantum systems, accommodating various types of noise models. We demonstrate its effectiveness by testing it both on simulated noisy circuits and on real quantum hardware.

Yuxuan Du, Yan Zhu, Yuan-Hang Zhang et al.

Efficient characterization of large-scale quantum systems, especially those produced by quantum analog simulators and megaquop quantum computers, poses a central challenge in quantum science due to the exponential scaling of the Hilbert space with respect to system size. Recent advances in artificial intelligence (AI), with its aptitude for high-dimensional pattern recognition and function approximation, have emerged as a powerful tool to address this challenge. A growing body of research has leveraged AI to represent and characterize scalable quantum systems, spanning from theoretical foundations to experimental realizations. Depending on how prior knowledge and learning architectures are incorporated, the integration of AI into quantum system characterization can be categorized into three synergistic paradigms: machine learning, and, in particular, deep learning and language models. This review discusses how each of these AI paradigms contributes to two core tasks in quantum systems characterization: quantum property prediction and the construction of surrogates for quantum states. These tasks underlie diverse applications, from quantum certification and benchmarking to the enhancement of quantum algorithms and the understanding of strongly correlated phases of matter. Key challenges and open questions are also discussed, together with future prospects at the interface of AI and quantum science.

Jiaxin Huang, Yan Zhu, Giulio Chiribella et al.

Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out for small quantum systems, the optimization becomes intractable as the system size grows large. To address this problem, we introduce a deep neural network with a sequence model architecture that searches for efficient measurement choices in a data-driven, adaptive manner. The model can be applied to a variety of tasks, including the prediction of linear and nonlinear properties of quantum states, as well as state clustering and state tomography tasks. In all these tasks, we find that the measurement choices identified by our neural network consistently outperform the uniformly random choice. Intriguingly, for topological quantum systems, our model tends to recommend measurements at the system's boundaries, even when the task is to predict bulk properties. This behavior suggests that the neural network may have independently discovered a connection between boundaries and bulk, without having been provided any built-in knowledge of quantum physics.

Yan Zhu, Ya-Dong Wu, Ge Bai et al.

Deep neural networks are a powerful tool for the characterization of quantum states. Existing networks are typically trained with experimental data gathered from the specific quantum state that needs to be characterized. But is it possible to train a neural network offline and to make predictions about quantum states other than the ones used for the training? Here we introduce a model of network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the states in the fiducial set. With little guidance of quantum physics, the network builds its own data-driven representation of quantum states, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representation produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter. Our network model provides a flexible approach that can be applied to online learning scenarios, where predictions must be generated as soon as experimental data become available, and to blind learning scenarios where the learner has only access to an encrypted description of the quantum hardware.

Giulio Chiribella, Xiao Yuan

Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as "device-independent". Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term "general probabilistic theories". With only a few exceptions, the two programmes on characterizing quantum correlations and characterizing quantum theory have so far proceeded on separate tracks, each one developing its own methods and its own agenda. This paper aims at bridging the gap, by comparing the two frameworks and illustrating how the two programmes can benefit each other.