Compact Neural-network Quantum State representations of Jastrow and Stabilizer states

AbstractQuantum 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 $$k$$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.

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The quantum entropy cone of hypergraphs

SciPost Physics ◽

10.21468/scipostphys.9.5.067 ◽

2020 ◽

Vol 9 (5) ◽

Author(s):

Ning Bao ◽

Newton Cheng ◽

Sergio Hernández-Cuenca ◽

Vincent P. Su

Keyword(s):

Quantum State ◽

Entanglement Entropy ◽

Quantum Entropy ◽

Graph Theoretic ◽

Tensor Networks ◽

Stabilizer States

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

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Mixed Quantum State Dynamics Estimation with Artificial Neural Network

2018 International Conference on Information and Communication Technology Convergence (ICTC) ◽

10.1109/ictc.2018.8539575 ◽

2018 ◽

Cited By ~ 1

Author(s):

Changjun Kim ◽

June-Koo Kevin Rhee ◽

Woojun Lee ◽

Jaewook Ahn

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Quantum State ◽

Artificial Neural

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Attention-based Quantum Tomography

Machine Learning: Science and Technology ◽

10.1088/2632-2153/ac362b ◽

2021 ◽

Author(s):

Peter Junghwa Cha ◽

Paul Ginsparg ◽

Felix Wu ◽

Juan Felipe Carrasquilla ◽

Peter L. McMahon ◽

...

Keyword(s):

Neural Network ◽

Natural Language Processing ◽

Natural Language ◽

Density Matrix ◽

Quantum State ◽

Language Processing ◽

Quantum Tomography ◽

Neural Network Models ◽

State Reconstruction ◽

Quantum State Reconstruction

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) 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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