Analog quantum simulators provide access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data is often hindered by measurement noise, limited observables, and incomplete knowledge of the underlying microscopic model. Here, we develop a machine learning approach based on a variational autoencoder (VAE) to analyze interference measurements of tunnel-coupled one-dimensional Bose gases, which realize the sine-Gordon quantum field theory. Trained in an unsupervised manner, the VAE learns a minimal latent representation that strongly correlates with the equilibrium control parameter of the system. Applied to non-equilibrium protocols, the latent space uncovers signatures of frozen-in solitons following rapid cooling, and reveals anomalous post-quench dynamics not captured by conventional correlation-based methods. These results demonstrate that generative models can extract physically interpretable variables directly from noisy and sparse experimental data, providing complementary probes of equilibrium and non-equilibrium physics in quantum simulators. More broadly, our work highlights how machine learning can supplement established field-theoretical techniques, paving the way for scalable, data-driven discovery in quantum many-body systems.

Hefei National Laboratory, Hefei 230088, China The computation of excited states in strongly interacting quantum many-body systems is of fundamental importance. Y et, it is notoriously challenging due to the exponential scaling of the Hilbert space dimension with the system size. Here, we introduce a neural network-based algorithm that can simultaneously output multiple low-lying excited states of a quantum many-body spin system in an accurate and efficient fashion. This algorithm, dubbed the neural quantum excited-state (NQES) algorithm, requires no explicit orthogonalization of the states and is generally applicable to higher dimensions. We demonstrate, through concrete examples including the Haldane-Shastry model with all-to-all interactions, that the NQES algorithm is capable of efficiently computing multiple excited states and their related observable expectations. In addition, we apply the NQES algorithm to two classes of long-range interacting trapped-ion systems in a two-dimensional Wigner crystal. For non-decaying all-to-all interactions with alternating signs, our computed low-lying excited states bear spatial correlation patterns similar to those of the ground states, which closely match recent experimental observations that the quasi-adiabatically prepared state accurately reproduces analytical ground-state correlations. For a system of up to 300 ions with power-law decaying antiferromagnetic interactions, we successfully uncover its gap scaling and correlation features. Our results establish a scalable and efficient algorithm for computing excited states of interacting quantum many-body systems, which holds potential applications ranging from benchmarking quantum devices to photoisomerization. Understanding interacting quantum many-body systems is a central task in a wide range of disciplines, from condensed matter physics, quantum chemistry to materials science [ 1 ]. For low-dimensional systems with short-range interactions, tensor-network-based methods have been successful in finding their ground states with area-law entanglement [ 2 - 5 ].

Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.

School of Physics, Sun Yat-sen University, Guangzhou 510275, China When computing the gradients of a quantum neural network using the parameter-shift rule, the cost function needs to be calculated twice for the gradient with respect to a single adjustable parameter of the network. When the total number of parameters is high, the quantum circuit for the computation has to be adjusted and run for many times. Here we propose an approach to compute all the gradients using a single circuit only, with a much reduced circuit depth and less classical registers. We also demonstrate experimentally, on both real quantum hardware and simulator, that our approach has the advantages that the circuit takes a significantly shorter time to compile than the conventional approach, resulting in a speedup on the total runtime. Artificial intelligence technology is making incredible total number of unique executed circuits could easily exceed progress nowadays.

With the rapid development of classical and quantum machine learning, a large number of machine learning frameworks have been proposed. However, existing machine learning frameworks usually only focus on classical or quantum, rather than both. Therefore, based on VQNet 1.0, we further propose VQNet 2.0, a new generation of unified classical and quantum machine learning framework that supports hybrid optimization. The core library of the framework is implemented in C++, and the user level is implemented in Python, and it supports deployment on quantum and classical hardware. In this article, we analyze the development trend of the new generation machine learning framework and introduce the design principles of VQNet 2.0 in detail: unity, practicality, efficiency, and compatibility, as well as full particulars of implementation. We illustrate the functions of VQNet 2.0 through several basic applications, including classical convolutional neural networks, quantum autoencoders, hybrid classical-quantum networks, etc. After that, through extensive experiments, we demonstrate that the operation speed of VQNet 2.0 is higher than the comparison method. Finally, through extensive experiments, we demonstrate that VQNet 2.0 can deploy on different hardware platforms, the overall calculation speed is faster than the comparison method. It also can be mixed and optimized with quantum circuits composed of multiple quantum computing libraries.

In popular culture, quantum computing is often painted as an ultra-powerful technology that will first outrace, and then replace, its classical counterpart. In reality, though, the two are inextricably linked. We use classical computation and simulations to develop and design today's nascent quantum devices, which are then nested within a much larger framework of classical computers. The effort to advance these different technologies – which both fuel and rely on each other – resembles something like a dance. Movement is required on both sides.