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arXiv:2507.09891

Sequence-Model-Guided Measurement Selection for Quantum State Learning

Jiaxin Huang, Yan Zhu, Giulio Chiribella, WU Ya

Published Jul 14, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2507.09891

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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.
Deep neural networks are a powerful tool for characterizing quantum states. Existing networks are typically trained with experimental data gathered from the quantum state that needs to be characterized. But is it possible to train a neural network offline, on a different set of states? Here we introduce a 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 fiducial states. With little guidance of quantum physics, the network builds its own data-driven representation of a quantum state, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representations 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.
We revisit quantum tomography in an informationally incomplete scenario and propose improved state reconstruction methods using deep neural networks. In the first approach, the trained network predicts an optimal linear or quadratic reconstructor with coefficients depending only on the collection of (already taken) measurement operators. This effectively refines the undercomplete tomographic reconstructor based on pseudoinverse operation. The second, based on an LSTM recurrent network performs state reconstruction sequentially. It can also optimize the measurement sequence, which suggests a no-free-lunch theorem for tomography: by narrowing the state space, we gain the possibility of more efficient tomography by learning the optimal sequence of measurements. Numerical experiments for a 2-qubit system show that both methods outperform standard maximum likelihood estimation and also scale to larger 3- and 4-qubit systems. Our results demonstrate that neural networks can effectively learn the underlying geometry of multi-qubit states and use it for their reconstruction.
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining the appropriate operations, however, generally requires information about the initial state of the system. Gathering this information becomes increasingly challenging when the initial state is not a priori known and the system’s size grows large. To address this problem, we develop a machine-learning algorithm that uses a small amount of measurement data to construct its internal representation of the system’s state. The algorithm compares this data-driven representation with a representation of the target state, and uses reinforcement learning to output the appropriate control operations. We illustrate the effectiveness of the algorithm showing that it achieves accurate control of unknown many-body quantum states and non-Gaussian continuous-variable states using data from a limited set of quantum measurements.
As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework for addressing this question in data-driven hadronic physics problems by developing diagnostic tools - centered on a quantitative quantum qualifier - that guide model selection between classical and quantum deep neural networks based on intrinsic properties of the data. Using controlled classification and regression studies, we show how relative model performance follows systematic trends in complexity, noise, and dimensionality, and how these trends can be distilled into a predictive criterion. We then demonstrate the utility of this approach through an application to Compton form factor extraction from deeply virtual Compton scattering, where the quantum qualifier identifies kinematic regimes favorable to quantum models. Together, these results establish a principled framework for deploying quantum machine-learning tools in precision hadronic physics.
Abstract Quantum state tomography is a daunting challenge of experimental quantum computing, even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine-learning method to recover the ground states of kkk k -local Hamiltonians from just the local information, where a fully connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems.
With increasing maturity of quantum computers, standard methods for characterizing global properties of their output quantum states via direct measurements and classical post-processing are becoming increasingly impractical due to large measurement costs. Although quantum neural networks could directly process quantum states to identify underlying characteristics with reduced measurement efforts, they often require deep quantum circuits that cannot be implemented on existing devices. To overcome these challenges, we introduce a hybrid quantum-classical neural network that consists of a shallow parameterized quantum circuit, measurements, and a classical neural network. The parameterized quantum circuit performs a nonlocal transformation of the measurement basis, which is jointly trained with the classical neural network to maximize the statistical distance between data obtained by measuring different quantum states. Using supervised learning, we demonstrate that the hybrid neural network distinguishes the topological phase of the surface code from a symmetry-enriched topological phase and random product states. Moreover, this hybrid neural network reduces both inference and training sample complexities of recognizing the topological phase by approximately one order of magnitude compared to a classical neural network trained on randomized Pauli measurements. As this hybrid neural network features a shallow quantum circuit that can be readily implemented on existing quantum computers, it enables the efficient characterization of complex quantum states.