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. There has been a growing interest in approaching the problem of quantum state reconstruction 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. AQT is based on the model proposed in ‘Attention is all you need’ by Vaswani et al (2017 NIPS) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing (NLP) 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 NLP captures the correlations among words in a sentence.
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. There has been a growing interest in approaching the problem of quantum state reconstruction 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. AQT is based on the model proposed in ‘Attention is all you need’ by Vaswani et al (2017 NIPS) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing (NLP) 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 NLP captures the correlations among words in a sentence.
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.
Attention mechanisms have revolutionized natural language processing. Combining them with quantum computing aims to further advance this technology. This paper introduces a novel Quantum Mixed-State Self-Attention Network (QMSAN) for natural language processing tasks. Our model leverages quantum computing principles to enhance the effectiveness of self-attention mechanisms. QMSAN uses a quantum attention mechanism based on mixed state, allowing for direct similarity estimation between queries and keys in the quantum domain. This approach leads to more effective attention coefficient calculations. We also propose an innovative quantum positional encoding scheme, implemented through fixed quantum gates within the circuit, improving the model's ability to capture sequence information without additional qubit resources. In numerical experiments of text classification tasks on public datasets, QMSAN outperforms Quantum Self-Attention Neural Network (QSANN). Furthermore, we demonstrate QMSAN's robustness in different quantum noise environments, highlighting its potential for near-term quantum devices.
Abstract Quantum state tomography is a crucial technique for characterizing the state of a quantum system, which is essential for many applications in quantum technologies. In recent years, there has been growing interest in leveraging neural networks to enhance the efficiency and accuracy of quantum state tomography. However, versatile methods that are broadly applicable across diverse reconstruction scenarios remain relatively underexplored. In this paper, we present two neural network-based approaches for both pure and mixed quantum state tomography: Restricted Feature Based Neural Network and Mixed States Neural Network, evaluate its effectiveness in comparison to existing neural network-based methods. We demonstrate that our proposed methods can achieve state-of-the-art results in reconstructing mixed quantum states from experimental data. Our work highlights the potential of neural networks in facilitating the development of quantum technologies. Source code is publicly available at https://github.com/luutn2002/uni-qst
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this article, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.
This article proposes a quantum self-attention neural network (QSAN) model that is implementable on parameterized quantum circuits (PQCs), providing a novel avenue for addressing natural language processing (NLP) tasks via quantum computing. The QSAN architecture comprises four blocks: the data preprocessing block, the quantum encoding block, the model design block, and the network optimization block. Through these blocks, classical text data are initially preprocessed and encoded into quantum states. The rich semantic features and intricate relationships within these quantum states are then captured and learned by a quantum self-attention layer and a quantum fully connected layer. Finally, the model performance is enhanced by optimizing the network parameters. Simulation results on publicly available topic classification and sentiment analysis datasets demonstrate that the QSAN model outperforms state-of-the-art baselines. As a limitation of the current study, these evaluations are restricted to a maximum sentence length of eight words due to simulation and hardware constraints. Moreover, the effectiveness, scalability, trainability, and robustness of the proposed model are comprehensively evaluated, highlighting its superior performance and potential for advanced NLP tasks.
Quantum-Inspired Transformers are a new class of approaches for natural language processing (NLP) that use principles inspired by physical quantum mechanics to encode and process linguistic information. Paper aims to improve both scalability and efficiency for large-scale NLP tasks in the next generation of artificial intelligence (AI). However, traditional transformers can struggle to encode complex semantic relationships across long sequences and can require high levels of compute resources, hence limiting scalability for large datasets and multilingual tasks. In addition, traditional embeddings do not represent multiple contextual meanings simultaneously, which decreases model expressiveness. To address these challenges and maximize the exploration of potential quantum effects in AI, this paper presents a Quantum State Embedding Attention (QSEA) framework that encodes tokens as quantum inspired states with complex-valued amplitudes. Attention, which is based on entangled states, is meant to efficiently capture long-range dependencies while reducing compute and increasing scalability, all without losing a rich understanding of context. Whereas multilingual translation needs to encode both the source similarity and the target language within a smaller semantic representation space. Our experimentation shows that QSEA consistently provides increased accuracy in decoding, measures attention across long sequences, and yields enduring scalability over large multilingual datasets. The evidence demonstrates the potential for QSEA to be the new layer in the future of AI systems, a layer that is scalable and a highperforming NLP application.