Publications

@book{Welling2026Generative,
  title = {Generative AI and Stochastic Thermodynamics: A Tale of Free Energies},
  author = {Welling, Max and Lu, Sirui and Holdijk, Lars},
  year = 2026,
  month = jul,
  publisher = {Cambridge University Press},
  address = {Cambridge},
  isbn = {9781009709064},
  url = {https://www.cambridge.org/core/books/generative-ai-and-stochastic-thermodynamics/A462AB4186719C2D4EBCC1F58A5D5764}
}

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@misc{Lu2026Agentic,
  title = {Agentic Publication Protocol: An Attempt to Modernize Scientific Publication},
  author = {Lu, Sirui and Qi, Xiao-Liang},
  year = 2026,
  month = jun,
  eprint = {2606.27386},
  archiveprefix = {arXiv},
  primaryclass = {cs.DL}
}

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Scientific publication is still organized primarily around static manuscripts, even though much of scientific progress depends on tacit know-how: how to run code, reproduce figures, interpret edge cases, choose useful follow-up directions, and avoid failed paths. Large language model agents create an opportunity to publish not only knowledge, but also operational know-how in a form that future readers and researchers can directly use. This paper outlines the Agentic Publication Protocol (APP), a lightweight repository format for packaging a paper together with code, data, environment information, reproducibility instructions, and an agent-facing instruction file. APP treats a version-controlled repository as the publication object and uses AGENTS.md and optional skills to define a paper agent that can explain the work, reproduce key results when possible, and support follow-up research. We describe the design principles and details of the protocol, as well as the agent skills useful for publishing papers under the protocol. We also describe development tools for evaluating and improving the protocol and associated agent skills. Finally, we provide a broader discussion of the future of scientific research in the agent era.

@misc{Molpeceres2026Benchmark,
  title = {Benchmark of Quantum Algorithms for Ground State Preparation in the Presence of Noise},
  author = {Molpeceres, Daniel and Lu, Sirui and Cirac, J. Ignacio and Kraus, Barbara},
  year = 2026,
  month = jun,
  eprint = {2606.20551},
  archiveprefix = {arXiv},
  primaryclass = {quant-ph}
}

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We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise. Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, we derive the scaling of the achievable relative energy as a function of the noise rate and support these results with numerical simulations. The Hamiltonian exhibits two phases, separated by a quantum phase transition. As expected, the performance of the different algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm, as proposed in [1], becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. We further present numerical results for the quantum approximate optimization algorithm [2], showing that it performs competitively with cooling in the trivial phase but is typically outperformed in the topological regime. Finally, we show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation. The analytical approach developed here, in conjunction with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.

@misc{Zhang2026Position,
  title = {Position: Science Is Collaborative --- LLM for Science Should Be Too},
  author = {Zhang, Terry Jingchen and Jiang, Wenyuan and Piedrahita, David Guzman and Yang, Yongjin and Lu, Sirui and Sch{\"o}lkopf, Bernhard and Jin, Zhijing},
  year = 2026,
  url = {https://openreview.net/forum?id=KHp9BwLQes}
}

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@misc{He2025CoDesigning,
  title = {Co-Designing Quantum Codes with Transversal Diagonal Gates via Multi-Agent Systems},
  author = {He, Xi and Lu, Sirui and Zeng, Bei},
  year = 2025,
  month = oct,
  eprint = {2510.20728},
  archiveprefix = {arXiv},
  primaryclass = {quant-ph}
}

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Exact scientific discovery requires more than heuristic search: candidate constructions must be turned into exact objects and checked independently. We extend TeXRA with an independent Lean 4 verification layer, turning it into a human-guided multi-agent platform that couples symbolic synthesis, combinatorial and linear-programming search, exact reconstruction of numerical candidates, and formal verification in Lean. Applying it to nonadditive quantum error-correcting codes with prescribed transversal diagonal gates, we obtain a Lean-certified catalogue of 14,116 distance-2 codes and resolve the transversal-T problem for several distance-3 codes, with all constructions, infinite families, and no-go results formalized and checked in Lean.

@article{Molpeceres2025Quantum,
  title = {Quantum Algorithms for Cooling: A Simple Case Study},
  author = {Molpeceres, Daniel and Lu, Sirui and Cirac, J. Ignacio and Kraus, Barbara},
  year = 2025,
  month = aug,
  journal = {Phys. Rev. Research},
  volume = {7},
  number = {3},
  pages = {033162},
  doi = {10.1103/4hx7-xnhw}
}

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Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for instance, on variational and adiabatic principles, or on dissipative state preparation. In this work, we investigate a set of cooling algorithms in a simple, solvable fermionic model which allows us to identify the mechanisms which underlie the cooling process and, also, those which prevent it. We derive analytical expressions for the cooling dynamics, steady states, and cooling rates in the weak coupling limit. We find that multi-frequency and randomized cycle strategies can significantly enhance the performance of the quantum algorithm and circumvent some of the obstacles. We also analyze the effects of noise and evaluate the conditions under which cooling remains feasible. Furthermore, we present optimized cooling protocols that can significantly enhance cooling performance in the presence of noise. Additionally, we compare cooling and dissipative state preparation and show that, in the model analyzed here, cooling generally achieves lower energies and is more resilient to noise.

@article{Lu2025Variational,
  title = {Variational Neural and Tensor Network Approximations of Thermal States},
  author = {Lu, Sirui and Giudice, Giacomo and Cirac, J. Ignacio},
  year = 2025,
  month = feb,
  journal = {Phys. Rev. B},
  volume = {111},
  number = {7},
  pages = {075102},
  doi = {10.1103/PhysRevB.111.075102}
}

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We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the ansatz expressiveness without accumulating errors from iterative imaginary time evolution. We employ a variety of trial states – both tensor networks as well as neural networks – as variational Ansätze for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to N=100 spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings.

@article{Jiang2024Vulnerability,
  title = {Adversarial Machine Learning Phases of Matter},
  author = {Jiang, Si and Lu, Sirui and Deng, Dong-Ling},
  year = 2023,
  month = dec,
  journal = {Quantum Front.},
  volume = {2},
  number = {1},
  pages = {15},
  doi = {10.1007/s44214-023-00043-z}
}

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We study the robustness of machine learning approaches to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial perturbations: adding a tiny amount of carefully crafted noises into the original legitimate examples will cause the classifiers to make incorrect predictions at a notably high confidence level. Through the lens of activation maps, we find that some important underlying physical principles and symmetries remain to be adequately captured for classifiers with even near-perfect performance. This explains why adversarial perturbations exist for fooling these classifiers. In addition, we find that, after adversarial training, the classifiers will become more consistent with physical laws and consequently more robust to certain kinds of adversarial perturbations. Our results provide valuable guidance for both theoretical and experimental future studies on applying machine learning techniques to condensed matter physics.

@article{Li2021Quantuma,
  title = {Quantum Federated Learning through Blind Quantum Computing},
  author = {Li, Weikang and Lu, Sirui and Deng, Dong-Ling},
  year = 2021,
  month = sep,
  journal = {Sci. China Phys. Mech. Astron.},
  volume = {64},
  number = {10},
  pages = {100312},
  doi = {10.1007/s11433-021-1753-3}
}

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Private distributed learning studies the problem of how multiple distributed entities collaboratively train a shared deep network with their private data unrevealed. With the security provided by the protocols of blind quantum computation, the cooperation between quantum physics and machine learning may lead to unparalleled prospect for solving private distributed learning tasks. In this paper, we introduce a quantum protocol for distributed learning that is able to utilize the computational power of the remote quantum servers while keeping the private data safe. For concreteness, we first introduce a protocol for private single-party delegated training of variational quantum classifiers based on blind quantum computing and then extend this protocol to multiparty private distributed learning incorporated with differential privacy. We carry out extensive numerical simulations with different real-life datasets and encoding strategies to benchmark the effectiveness of our protocol. We find that our protocol is robust to experimental imperfections and is secure under the gradient attack after the incorporation of differential privacy. Our results show the potential for handling computationally expensive distributed learning tasks with privacy guarantees, thus providing a valuable guide for exploring quantum advantages from the security perspective in the field of machine learning with real-life applications.

@article{Hou2020Determining,
  title = {Determining System Hamiltonian from Eigenstate Measurements without Correlation Functions},
  author = {Hou, Shi-Yao and Cao, Ningping and Lu, Sirui and Shen, Yi and Poon, Yiu-Tung and Zeng, Bei},
  year = 2020,
  month = sep,
  journal = {New J. Phys.},
  volume = {22},
  number = {8},
  pages = {083088},
  doi = {10.1088/1367-2630/abaacf}
}

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Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on the eigenstate, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameters, with only polynomial number of parameters in terms of system size. We also develop a machine learning-based-method to solve the first-order gradient used in the algorithm. Our method is tested numerically for randomly generated local Hamiltonians and returns promising reconstruction in the desired accuracy. Our result shed light on the fundamental question on how a single eigenstate can encode the full system Hamiltonian, indicating a somewhat surprising answer that only local measurements are enough without additional assumptions, for generic cases.

@article{Lu2020Quantum,
  title = {Quantum Adversarial Machine Learning},
  author = {Lu, Sirui and Duan, Lu-Ming and Deng, Dong-Ling},
  year = 2020,
  month = aug,
  journal = {Phys. Rev. Research},
  volume = {2},
  number = {3},
  pages = {033212},
  doi = {10.1103/physrevresearch.2.033212}
}

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Adversarial machine learning studies vulnerabilities of machine-learning models in adversarial settings and develops techniques to make learning robust. We show that quantum classifiers, like their classical counterparts, are vulnerable to adversarial examples: adding carefully crafted, imperceptible perturbations to legitimate inputs leads to misclassification, demonstrated for classifying real-life images, phases of matter, and quantum data. We also show that practical defense strategies can be designed to counter a range of such attacks, bridging machine learning and quantum physics and offering guidance for implementing quantum classifiers on near-term and future quantum devices.

@article{Xin2019Localmeasurementbased,
  title = {Local-Measurement-Based Quantum State Tomography via Neural Networks},
  author = {Xin, Tao and Lu, Sirui and Cao, Ningping and Anikeeva, Galit and Lu, Dawei and Li, Jun and Long, Guilu and Zeng, Bei},
  year = 2019,
  month = dec,
  journal = {npj Quantum Inf.},
  volume = {5},
  number = {1},
  pages = {109},
  doi = {10.1038/s41534-019-0222-3}
}

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Quantum 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 full quantum state from its 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.

@article{Li2019Quantum,
  title = {Quantum Spacetime on a Quantum Simulator},
  author = {Li, Keren and Li, Youning and Han, Muxin and Lu, Sirui and Zhou, Jie and Ruan, Dong and Long, Gui-Lu and Wan, Yidun and Lu, Dawei and Zeng, Bei and Laflamme, Raymond},
  year = 2019,
  month = dec,
  journal = {Commun. Phys.},
  volume = {2},
  number = {1},
  pages = {122},
  doi = {10.1038/s42005-019-0218-5}
}

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We experimentally simulate the spin networks – a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra comprises spin networks. In this initial attempt to study quantum spacetime by quantum information processing, on a four-qubit nuclear magnetic resonance quantum simulator, we simulate the basic module – comprising five quantum tetrahedra – of the interactions of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulate their interactions, our experiment serves as the basic module that represents the Feynman diagram vertex in the spin-network formulation of quantum spacetime.

@article{Lian2019Machine,
  title = {Machine Learning Topological Phases with a Solid-State Quantum Simulator},
  author = {Lian, Wenqian and Wang, Sheng-Tao and Lu, Sirui and Huang, Yuanyuan and Wang, Fei and Yuan, Xinxing and Zhang, Wengang and Ouyang, Xiaolong and Wang, Xin and Huang, Xianzhi and He, Li and Chang, Xiuying and Deng, Dong-Ling and Duan, Luming},
  year = 2019,
  month = may,
  journal = {Phys. Rev. Lett.},
  volume = {122},
  number = {21},
  pages = {210503},
  doi = {10.1103/physrevlett.122.210503}
}

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We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks – a class of deep feed-forward artificial neural networks with widespread applications in machine learning – can be trained to successfully identify different topological phases protected by chiral symmetry from experimental raw data generated with a solid-state quantum simulator. Our results explicitly showcase the exceptional power of machine learning in the experimental detection of topological phases, which paves a way to study rich topological phenomena with the machine learning toolbox.

@misc{Niu2019Optimizing,
  title = {Optimizing QAOA: Success Probability and Runtime Dependence on Circuit Depth},
  author = {Niu, Murphy Yuezhen and Lu, Sirui and Chuang, Isaac L.},
  year = 2019,
  month = may,
  eprint = {1905.12134},
  archiveprefix = {arXiv},
  primaryclass = {quant-ph}
}

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The quantum approximate optimization algorithm (QAOA) first proposed by Farhi et al. promises near-term applications based on its simplicity, universality, and provable optimality. A depth-p QAOA consists of p interleaved unitary transformations induced by two mutually non-commuting Hamiltonians. A long-standing question concerning the performance of QAOA is the dependence of its success probability as a function of circuit depth p. We make initial progress by analyzing the success probability of QAOA for realizing state transfer in a one-dimensional qubit chain using two-qubit XY Hamiltonians and single-qubit Hamiltonians. We provide analytic state transfer success probability dependencies on p in both low and large p limits by leveraging the unique spectral property of the XY Hamiltonian. We support our proof under a given QAOA ansatz with numerical optimizations of QAOA for up to N=20 qubits. We show that the optimized QAOA can achieve the well-known quadratic speedup, Grover speedup, over the classical alternatives. Treating QAOA optimization as a quantum control problem, we also provide numerical evidence of how the circuit depth determines the controllability of the QAOA ansatz.

@article{Lu2019Efficient,
  title = {Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines},
  author = {Lu, Sirui and Gao, Xun and Duan, L.-M.},
  year = 2019,
  month = apr,
  journal = {Phys. Rev. B},
  volume = {99},
  number = {15},
  pages = {155136},
  doi = {10.1103/physrevb.99.155136}
}

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Representation by neural networks, in particular by restricted Boltzmann machines (RBM), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of quantum states can be efficiently represented with the RBM. Here, we show that the RBM can efficiently represent a wide class of many-body entangled states with rich exotic topological orders. This includes: (1) ground states of double semion and twisted quantum double models with intrinsic topological orders; (2) states of the AKLT model and 2D CZX model with symmetry protected topological order; (3) states of Haah code model with fracton topological order; (4) generalized stabilizer states and hypergraph states that are important for quantum information protocols. One twisted quantum double model state considered here harbors non-abelian anyon excitations. Our result shows that it is possible to study a variety of quantum models with exotic topological orders and rich physics using the RBM computational toolbox.

@article{Lu2018Separabilityentanglement,
  title = {Separability-Entanglement Classifier via Machine Learning},
  author = {Lu, Sirui and Huang, Shilin and Li, Keren and Li, Jun and Chen, Jianxin and Lu, Dawei and Ji, Zhengfeng and Shen, Yi and Zhou, Duanlu and Zeng, Bei},
  year = 2018,
  month = jul,
  journal = {Phys. Rev. A},
  volume = {98},
  number = {1},
  pages = {012315},
  doi = {10.1103/physreva.98.012315}
}

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The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial transpose (PPT) criterion and the k-symmetric extendibility criterion to tackle this problem in practice, none of them enables a general, effective solution to the problem even for small dimensions. Explicitly, separable states form a high-dimensional convex set, which exhibits a vastly complicated structure. In this work, we build a new separability-entanglement classifier underpinned by machine learning techniques. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum entanglement via the machine learning approach.

@article{Xin2018NMRCloudQ,
  title = {NMRCloudQ: A Quantum Cloud Experience on a Nuclear Magnetic Resonance Quantum Computer},
  author = {Xin, Tao and Huang, Shilin and Lu, Sirui and Li, Keren and Luo, Zhihuang and Yin, Zhangqi and Li, Jun and Lu, Dawei and Long, Gui-Lu and Zeng, Bei},
  year = 2018,
  month = jan,
  journal = {Sci. Bull.},
  volume = {63},
  number = {1},
  pages = {17},
  doi = {10.1016/j.scib.2017.12.022}
}

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As of today, no one can tell when a universal quantum computer with thousands of logical quantum bits (qubits) will be built. At present, most quantum computer prototypes involve less than ten individually controllable qubits, and only exist in laboratories for the sake of either the great costs of devices or professional maintenance requirements. Moreover, scientists believe that quantum computers will never replace our daily, every-minute use of classical computers, but would rather serve as a substantial addition to the classical ones when tackling some particular problems. Due to the above two reasons, cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms has followed up yet. Here, we report our new cloud quantum computing service – NMRCloudQ, where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. In our current version, four qubits are already usable with an average 1.26% single-qubit gate error rate and 1.77% two-qubit controlled-NOT gate error rate via randomized benchmarking tests. Improved control precisions as well as a new seven-qubit processor are also in preparation and will be available later.

@inproceedings{Grassl2017Codes,
  title = {Codes for Simultaneous Transmission of Quantum and Classical Information},
  author = {Grassl, Markus and Lu, Sirui and Zeng, Bei},
  year = 2017,
  booktitle = {IEEE International Symposium on Information Theory (ISIT)},
  pages = {1718--1722},
  doi = {10.1109/isit.2017.8006823}
}

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We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as `hybrid codes'. We construct hybrid codes [[n,k: m,d]]_q with length n and distance d, that simultaneously transmit k qudits and m symbols from a classical alphabet of size q. Many good codes such as [[7,1: 1,3]]_2, [[9,2: 2,3]]_2, [[10,3: 2,3]]_2, [[11,4: 2,3]]_2, [[11,1: 2,4]]_2, [[13,1: 4,4]]_2, [[13,1: 1,5]]_2, [[14,1: 2,5]]_2, [[15,1: 3,5]]_2, [[19,9: 1,4]]_2, [[20,9: 2,4]]_2, [[21,9: 3,4]]_2, [[22,9: 4,4]]_2 have been found. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum codes.