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arXiv:2212.04940

Quantum State Tomography Inspired by Language Modeling

Lu Zhong, Chu Guo, Xiaoting Wang

Published Dec 9, 2022• 5 citations
arXivHTMLPDF

Abstract

Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially growing complexity. In this work, we propose a scalable solution by considering state tomography as a language modeling task, where the unknown quantum state is treated as an unknown language, the correlation of the quantum state is interpreted as the semantic information specific to this language, and the measurement outcomes are simply the text instances generated from the language. Based on a customized transformer model from language modeling, we demonstrate that our method can accurately reconstruct prototypical pure and mixed quantum states using less samples than state-of-the-art methods. More importantly, our method can reconstruct a class of similar states simultaneously, in comparison with the existing neural network methods that need to train a model for each unknown state.

DOI
10.48550/arxiv.2212.04940

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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.