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Attention-based Quantum Tomography

Peter Cha, Paul Ginsparg, Felix Wu, Juan Carrasquilla, Peter L. McMahon, Eun-Ah Kim

arXiv:2006.12469v3quant-phcs.LG

TL;DR

Exact tomography of Nq-qubit many-body states requires data and processing that grow exponentially with system size, limiting exact density-matrix reconstruction to small systems. AQT adapts a Transformer generative model to learn distributions of POVM outcomes and reconstruct a quantum state's density matrix. AQT improved sample complexity over RNN tomography and reconstructed IBMQ’s noisy 3-qubit GHZ state in qualitative agreement with MLE (fidelity 0.917 vs 0.897).

  • Problem

    Exact tomography of Nq-qubit many-body states requires data and processing that grow exponentially with system size, limiting exact density-matrix reconstruction to small systems.

    Source: p. 1

  • Method

    AQT adapts a Transformer generative model to learn distributions of POVM outcomes and reconstruct a quantum state's density matrix.

    Source: pp. 1–2

  • Results

    AQT improved sample complexity over RNN tomography and reconstructed IBMQ’s noisy 3-qubit GHZ state in qualitative agreement with MLE (fidelity 0.917 vs 0.897).

    Source: pp. 4–5

  • Takeaways & Limitations

    AQT is designed for experimentally realizable local POVMs and requires neither globally acting gates nor assumptions about the state's entanglement structure or purity.

    Source: p. 6

    The study is largely GHZ-based; more complex entanglement and larger experimental systems remain to be tested to establish AQT's scalability.

    Source: p. 6

Abstract

from arXiv · show

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.

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