Attention-based Quantum Tomography

Abstract

With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. Recent works found promise in recasting the problem of quantum state reconstruction to learning the probability distribution of quantum state measurement vectors using generative neural network models. Here we propose the "Attention-based Quantum Tomography" (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. The AQT is based on the model proposed in "Attention is all you need" by Vishwani et al ( 2017) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for natural language processing captures the correlations among words in a sentence.

Bidirectional information flow quantum state tomography

“…3. Compared with the state-of-the-art RNN-QST [17] and AQT [19] methods, our BiGRU-QST method uses almost the fewest number of measurement samples to achieve over 99% fidelity. We can see also that a linear growth of the number of training samples with respect to the number of qubits.…”

“…Based on the powerful autoregressive model Recurrent Neural Networks (RNN), Carrasquilla et al [17] introduced RNN-QST, which is able to use the informationally complete (IC) positive-operator valued measures (POVMs) samples, to reconstruct quantum states with high classical fidelity. There is also a transformer [18] QST method based on attention mechanism-based generative network, which reconstructs mixed state density matrix of a noisy quantum state [19]. Moreover, there are some other QST methods driven by generative models [20,21].…”

“…At the same time, we propose a network training standard to conduct early stopping, which can help one to find effectively better training model using fewer training samples. These methods enable us to use fewer quantum state measurement samples than RNN [17] and AQT [19] neural network tomography to achieve over 99% classical fidelity on GHZ state. We test our method in dealing with "easy quantum states" and "hard quantum states" that have different sampling difficulty [22].…”

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

“…Modern incarnations of autoregressive models include, among others, recurrent neural networks (RNN) [69,70], Pixel Convolutional Neural Networks (PixelCNN) [71], Transformers [67]. Recent work has effectively applied these models to quantum systems [50,51,65,66,72]. Here, we use an autoregressive Transformer, which follows the same architecture as the model in [66].…”

Hamiltonian-Driven Shadow Tomography of Quantum States

“…It aims to reconstruct the density matrix from repeated measurements of identically prepared copies of a quantum system. While the complexity of exact tomography of the full density matrix scales exponentially with the system size due to the curse of dimensionality [6,7], approximate tomography with polynomial complexity has been developed with assumptions of the underlying quantum state, including matrix product state tomography [8][9][10], reduced density matrix tomography [11][12][13][14][15][16], and machine learning tomography [17][18][19][20][21][22][23][24][25].…”