Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.14714

Denoising quantum states with Quantum Autoencoders -- Theory and Applications

Tom Achache, Lior Horesh C, John A. Smolin

Published Dec 29, 2020• 5 citations
arXivHTMLPDF

Abstract

We implement a Quantum Autoencoder (QAE) as a quantum circuit capable of correcting Greenberger-Horne-Zeilinger (GHZ) states subject to various noisy quantum channels : the bit-flip channel and the more general quantum depolarizing channel. The QAE shows particularly interesting results, as it enables to perform an almost perfect reconstruction of noisy states, but can also, more surprisingly, act as a generative model to create noise-free GHZ states. Finally, we detail a useful application of QAEs : Quantum Secret Sharing (QSS). We analyze how noise corrupts QSS, causing it to fail, and show how the QAE allows the QSS protocol to succeed even in the presence of noise.

DOI
10.48550/arxiv.2012.14714

Related papers

Quantum Autoencoders to Denoise Quantum Data

Dmytro Bondarenko, Polina Feldmann

Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders-neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.

arXiv:1910.09169•Physical Review Letters•Mar 31, 2020•117 citations

Reconstructing a quantum state with a variational autoencoder

Chuangtao Chen, Zhimin He, Zhiming Huang +1 more

Quantum state tomography (QST) is an important and challenging task in the field of quantum information, which has attracted a lot of attentions in recent years. Machine learning models can provide a classical representation of the quantum state after trained on the measurement outcomes, which are part of effective techniques to solve QST problem. In this work, we use a variational autoencoder (VAE) to learn the measurement distribution of two quantum states generated by MPS circuits. We first consider the Greenberger–Horne–Zeilinger (GHZ) state which can be generated by a simple MPS circuit. Simulation results show that a VAE can reconstruct 3- to 8-qubit GHZ states with a high fidelity, i.e., 0.99, and is robust to depolarizing noise. The minimum number ([Formula: see text]) of training samples required to reconstruct the GHZ state up to 0.99 fidelity scales approximately linearly with the number of qubits ([Formula: see text]). However, for the quantum state generated by a complex MPS circuit, [Formula: see text] increases exponentially with [Formula: see text], especially for the quantum state with high entanglement entropy.

International Journal of Quantum Information•Dec 1, 2021•8 citations

Self-correcting quantum teleportation protocol

Bayu Dwi Hatmoko, Muhammad Taufiqi, Agus Purwanto +2 more

In this work, we propose a self-correcting quantum teleportation protocol capable of transmitting a three-qubit Greenberger-Horne-Zeilinger-type (GHZ-type) state through a four-qubit quantum state in the presence of collective Bit-Flip Noise. We show that the protocol can self-correct the noise effect on the teleportation process, resulting in perfect state transfer with unit fidelity and probability. We also show that the proposed protocol has up to 33.3% lower quantum gate resource cost than a conventional combination of quantum error correction and teleportation protocols. Furthermore, we discuss the protocol’s generalization in teleporting [Formula: see text]-qubit GHZ-type state, with [Formula: see text] being any integer. Lastly, we simulate the proposed protocol under the noise in Qiskit and show that it can be implemented well.

International Journal of Quantum Information•Jul 30, 2025•0 citations

Noisy intermediate-scale quantum computer–compatible error correction of quantum data using modified dissipative quantum neural networks

Armin Ahmadkhaniha, M. Bathaee

Using a dissipative quantum neural network (DQNN) accompanied by conjugate layers, we upgrade the performance of the existing quantum autoencoder (QAE) network as a quantum denoiser of a noisy $m$-qubit GHZ state. Our denoising architecture requires a much smaller number of learning parameters, which can decrease the training time, especially when a deep or stacked DQNN is needed to approach the highest fidelity in the noisy intermediate-scale quantum era. In QAE, we reduce the connection between the hidden layer's qubits and the output's qubits to modify the decoder. The Renyi entropy of the hidden and output qubits' states is analyzed with respect to other qubits during learning iterations. During the learning process, if the hidden layer remains connected to the input layers, the network can almost perfectly denoise unseen noisy data with a different underlying noise distribution using the learning parameters acquired from training data.

Physical Review A•Mar 25, 2024•1 citation

Cryptanalysis of quantum secret sharing based on GHZ states

Xiao-Fen Liu, Ri-Jing Pan

In a recent paper (Hwang et al 2011 Phys. Scr. 83 045004), a subtle quantum secret sharing (QSS) protocol was proposed. One major advantage of this protocol is its high efficiency; that is, it is more efficient than other QSS protocols using the Greenberger–Horne–Zeilinger states. However, we analyzed the security of this protocol and found that it is insecure for one agent who may deduce half of the information about the deal's secret directly just by his/her piece of secret. Finally, a feasible improvement of this QSS protocol is put forward.

Physica Scripta•Sep 27, 2011•11 citations

Practical multipartite entanglement distribution in noisy channels

Mei-Yu Wang, Hao Guo, Fengli Yan +1 more

Entanglement among multiple parties is vital for practical quantum information applications. Astwo kinds of typical multipartite entangled state, the W and Greenberger-Horne-Zeilinger (GHZ)states have attracted a lot of attention. In this paper, we propose two practical linear optical schemes for multipartite entanglement distribution in noisy channels. Using the time-bin or spatial-mode degree of freedom (DoF) encoding, the influence of the noise will be eliminated and perfect W or GHZ state can be achieved among different nodes in a deterministic way. Moreover, we construct quantum circuits, which can be implemented with current technology. These results contribute to long-distance quantum communication both in theoretical and experimental points of view.

Results in Physics•Jul 20, 2022•5 citations
We implement a Quantum Autoencoder (QAE) as a quantum circuit capable of correcting Greenberger-Horne-Zeilinger (GHZ) states subject to various noisy quantum channels : the bit-flip channel and the more general quantum depolarizing channel. The QAE shows particularly interesting results, as it enables to perform an almost perfect reconstruction of noisy states, but can also, more surprisingly, act as a generative model to create noise-free GHZ states. Finally, we detail a useful application of QAEs : Quantum Secret Sharing (QSS). We analyze how noise corrupts QSS, causing it to fail, and show how the QAE allows the QSS protocol to succeed even in the presence of noise.
Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders-neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.
Quantum state tomography (QST) is an important and challenging task in the field of quantum information, which has attracted a lot of attentions in recent years. Machine learning models can provide a classical representation of the quantum state after trained on the measurement outcomes, which are part of effective techniques to solve QST problem. In this work, we use a variational autoencoder (VAE) to learn the measurement distribution of two quantum states generated by MPS circuits. We first consider the Greenberger–Horne–Zeilinger (GHZ) state which can be generated by a simple MPS circuit. Simulation results show that a VAE can reconstruct 3- to 8-qubit GHZ states with a high fidelity, i.e., 0.99, and is robust to depolarizing noise. The minimum number ([Formula: see text]) of training samples required to reconstruct the GHZ state up to 0.99 fidelity scales approximately linearly with the number of qubits ([Formula: see text]). However, for the quantum state generated by a complex MPS circuit, [Formula: see text] increases exponentially with [Formula: see text], especially for the quantum state with high entanglement entropy.
In this work, we propose a self-correcting quantum teleportation protocol capable of transmitting a three-qubit Greenberger-Horne-Zeilinger-type (GHZ-type) state through a four-qubit quantum state in the presence of collective Bit-Flip Noise. We show that the protocol can self-correct the noise effect on the teleportation process, resulting in perfect state transfer with unit fidelity and probability. We also show that the proposed protocol has up to 33.3% lower quantum gate resource cost than a conventional combination of quantum error correction and teleportation protocols. Furthermore, we discuss the protocol’s generalization in teleporting [Formula: see text]-qubit GHZ-type state, with [Formula: see text] being any integer. Lastly, we simulate the proposed protocol under the noise in Qiskit and show that it can be implemented well.
Using a dissipative quantum neural network (DQNN) accompanied by conjugate layers, we upgrade the performance of the existing quantum autoencoder (QAE) network as a quantum denoiser of a noisy mmm-qubit GHZ state. Our denoising architecture requires a much smaller number of learning parameters, which can decrease the training time, especially when a deep or stacked DQNN is needed to approach the highest fidelity in the noisy intermediate-scale quantum era. In QAE, we reduce the connection between the hidden layer's qubits and the output's qubits to modify the decoder. The Renyi entropy of the hidden and output qubits' states is analyzed with respect to other qubits during learning iterations. During the learning process, if the hidden layer remains connected to the input layers, the network can almost perfectly denoise unseen noisy data with a different underlying noise distribution using the learning parameters acquired from training data.
In a recent paper (Hwang et al 2011 Phys. Scr. 83 045004), a subtle quantum secret sharing (QSS) protocol was proposed. One major advantage of this protocol is its high efficiency; that is, it is more efficient than other QSS protocols using the Greenberger–Horne–Zeilinger states. However, we analyzed the security of this protocol and found that it is insecure for one agent who may deduce half of the information about the deal's secret directly just by his/her piece of secret. Finally, a feasible improvement of this QSS protocol is put forward.
Entanglement among multiple parties is vital for practical quantum information applications. Astwo kinds of typical multipartite entangled state, the W and Greenberger-Horne-Zeilinger (GHZ)states have attracted a lot of attention. In this paper, we propose two practical linear optical schemes for multipartite entanglement distribution in noisy channels. Using the time-bin or spatial-mode degree of freedom (DoF) encoding, the influence of the noise will be eliminated and perfect W or GHZ state can be achieved among different nodes in a deterministic way. Moreover, we construct quantum circuits, which can be implemented with current technology. These results contribute to long-distance quantum communication both in theoretical and experimental points of view.