"[4] Deutsch, David, et al. \"Quantum privacy amplification and the security of quantum cryptography over noisy channels.\" [Physical Review Letters 77.13 (1996): 2818.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.77.2818)\n",
"\n",
"[5] Jin, Rui-Bo, et al. \"Highly efficient entanglement swapping and teleportation at telecom wavelength.\" [Scientific reports 5.1 (2015): 1-7.](https://www.nature.com/articles/srep09333)\n",
"[5] Zeilinger, Anton, et al. \"Three-particle entanglements from two entangled pairs.\" [Physical Review Letters 78.16 (1997): 3031.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.78.3031)\n",
"\n",
"[6] Carleo, Giuseppe, and Matthias Troyer. \"Solving the quantum many-body problem with artificial neural networks.\" [Science 355.6325 (2017): 602-606.](https://science.sciencemag.org/content/355/6325/602)\n",
"[6] Zukowski, Marek, et al. \"\" Event-ready-detectors\" Bell experiment via entanglement swapping.\" [Physical Review Letters 71.26 (1993).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.4287)\n",
"\n",
"[7] Senior, Andrew W., et al. \"Improved protein structure prediction using potentials from deep learning.\" [Nature 577.7792 (2020): 706-710.](https://www.nature.com/articles/s41586-019-1923-7)\n",
"[7] Carleo, Giuseppe, and Matthias Troyer. \"Solving the quantum many-body problem with artificial neural networks.\" [Science 355.6325 (2017): 602-606.](https://science.sciencemag.org/content/355/6325/602)\n",
"\n",
"[8] Senior, Andrew W., et al. \"Improved protein structure prediction using potentials from deep learning.\" [Nature 577.7792 (2020): 706-710.](https://www.nature.com/articles/s41586-019-1923-7)\n",
"These protocols look quite simple, but things could become extremely complicated when many parties communicate with each other for multiple rounds and we still need to find out the best local operations each party should apply in each round. Now, we should at least have a taste of why designing an LOCC protocol is challenging. With such difficulty, many practical LOCC protocols have been purposed to fulfill meaningful tasks including entanglement distillation [3-4], entanglement swapping [5], and so on.\n",
"These protocols look quite simple, but things could become extremely complicated when many parties communicate with each other for multiple rounds and we still need to find out the best local operations each party should apply in each round. Now, we should at least have a taste of why designing an LOCC protocol is challenging. With such difficulty, many practical LOCC protocols have been purposed to fulfill meaningful tasks including entanglement distillation [3-4], entanglement swapping [5-6], and so on.\n",
"\n"
]
},
...
...
@@ -48,7 +48,7 @@
"source": [
"## Philosophy of LOCCNet\n",
"\n",
"Inspired by the success of Machine Learning (ML) in solving the quantum many-body problem [6] and protein folding structure prediction [7], we would like to adopt the learning capability of ML to help search optimal LOCC protocols among many possible combinations. The basic idea of LOCCNet is to utilize quantum neural networks (QNNs) to represent each local quantum operation $\\mathcal{E}^{(k)}_j$. That means each node represented in the tree graph of an LOCC protocol is now replaced by a QNN, which is essentially a parametrize quantum circuit (PQC) denoted by $U(\\boldsymbol \\theta)$. In Paddle Quantum, we already provide many QNN templates to reduce the learning cost for users. Once we set up the QNN, we can freely choose the measurement and communication plan. One last recipe we would need is a learning objective which is usually encoded as a loss function $L$. For example in quantum teleportation, the learning objective could be maximizing the state fidelity between Alice's state $|\\psi\\rangle$ and the state Bob receives $|\\phi\\rangle$ under four possible measurement results, meaning that $L \\equiv \\sum_{m_1m_2} \\big(1- F(|\\psi\\rangle, |\\phi\\rangle)\\big)$. The loss function should be designed according to the specific goal we want to accomplish. Finally, classical optimization methods (mainly gradient-based) will be applied to train the parameters in each QNN. Once the optimization has been done, we could obtain a near-optimal LOCC protocol. From our perspective, such a framework could sharply reduce the efforts to develop novel LOCC protocols, and the results should be easy to verify by experiments.\n",
"Inspired by the success of Machine Learning (ML) in solving the quantum many-body problem [7] and protein folding structure prediction [8], we would like to adopt the learning capability of ML to help search optimal LOCC protocols among many possible combinations. The basic idea of LOCCNet is to utilize quantum neural networks (QNNs) to represent each local quantum operation $\\mathcal{E}^{(k)}_j$. That means each node represented in the tree graph of an LOCC protocol is now replaced by a QNN, which is essentially a parametrize quantum circuit (PQC) denoted by $U(\\boldsymbol \\theta)$. In Paddle Quantum, we already provide many QNN templates to reduce the learning cost for users. Once we set up the QNN, we can freely choose the measurement and communication plan. One last recipe we would need is a learning objective which is usually encoded as a loss function $L$. For example in quantum teleportation, the learning objective could be maximizing the state fidelity between Alice's state $|\\psi\\rangle$ and the state Bob receives $|\\phi\\rangle$ under four possible measurement results, meaning that $L \\equiv \\sum_{m_1m_2} \\big(1- F(|\\psi\\rangle, |\\phi\\rangle)\\big)$. The loss function should be designed according to the specific goal we want to accomplish. Finally, classical optimization methods (mainly gradient-based) will be applied to train the parameters in each QNN. Once the optimization has been done, we could obtain a near-optimal LOCC protocol. From our perspective, such a framework could sharply reduce the efforts to develop novel LOCC protocols, and the results should be easy to verify by experiments.\n",
"\n",
"\n",
"**Note:** LOCCNet only supports density matrix formulation at the current version."
...
...
@@ -140,11 +140,14 @@
"\n",
"[4] Deutsch, David, et al. \"Quantum privacy amplification and the security of quantum cryptography over noisy channels.\" [Physical Review Letters 77.13 (1996): 2818.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.77.2818)\n",
"\n",
"[5] Jin, Rui-Bo, et al. \"Highly efficient entanglement swapping and teleportation at telecom wavelength.\" [Scientific reports 5.1 (2015): 1-7.](https://www.nature.com/articles/srep09333)\n",
"[5] Zeilinger, Anton, et al. \"Three-particle entanglements from two entangled pairs.\" [Physical Review Letters 78.16 (1997): 3031.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.78.3031)\n",
"\n",
"[6] Carleo, Giuseppe, and Matthias Troyer. \"Solving the quantum many-body problem with artificial neural networks.\" [Science 355.6325 (2017): 602-606.](https://science.sciencemag.org/content/355/6325/602)\n",
"[6] Zukowski, Marek, et al. \"\" Event-ready-detectors\" Bell experiment via entanglement swapping.\" [Physical Review Letters 71.26 (1993).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.4287)\n",
"\n",
"[7] Carleo, Giuseppe, and Matthias Troyer. \"Solving the quantum many-body problem with artificial neural networks.\" [Science 355.6325 (2017): 602-606.](https://science.sciencemag.org/content/355/6325/602)\n",
"\n",
"[8] Senior, Andrew W., et al. \"Improved protein structure prediction using potentials from deep learning.\" [Nature 577.7792 (2020): 706-710.](https://www.nature.com/articles/s41586-019-1923-7)\n",
"\n",
"[7] Senior, Andrew W., et al. \"Improved protein structure prediction using potentials from deep learning.\" [Nature 577.7792 (2020): 706-710.](https://www.nature.com/articles/s41586-019-1923-7)\n",
