by topics
Publications grouped by research topic, in reverse chronological order of release within each topic.
An up-to-date list is available on Google Scholar. An asterisk (*) after my name indicates papers whose authors are ordered alphabetically or contributed equally as co-first authors.
Learning and Characterizing Quantum Systems
- Learning Arbitrary Lindbladians from Time EvolutionZhili Chen and Zhan Yu*Jul 2026
@misc{CY26, title = {Learning Arbitrary Lindbladians from Time Evolution}, author = {Chen, Zhili and Yu, Zhan}, year = {2026}, month = jul, primaryclass = {quant-ph}, publisher = {arXiv}, url = {https://arxiv.org/abs/2607.28610}, } - Near-Optimal Learning of Local LindbladiansJun 2026
@misc{ACG+26, title = {Near-Optimal Learning of Local Lindbladians}, author = {Arad, Itai and Chen, Zhili and Guo, Naixu and Rebentrost, Patrick and Yu, Zhan}, year = {2026}, month = jun, primaryclass = {quant-ph}, publisher = {arXiv}, url = {http://arxiv.org/abs/2606.20535}, } - Amortized Stabilizer Rényi Entropy of Quantum DynamicsSep 2024
@misc{ZCS+24, title = {Amortized {{Stabilizer R{\'e}nyi Entropy}} of {{Quantum Dynamics}}}, author = {Zhu, Chengkai and Chen, Yu-Ao and Shen, Zanqiu and Liu, Zhiping and Yu, Zhan and Wang, Xin}, year = {2024}, month = sep, primaryclass = {quant-ph}, publisher = {arXiv}, url = {https://arxiv.org/abs/2409.06659}, } - Efficient Information Recovery from Pauli Noise via Classical ShadowMay 2023
The rapid advancement of quantum computing has led to an extensive demand for effective techniques to extract classical information from quantum systems, particularly in fields like quantum machine learning and quantum chemistry. However, quantum systems are inherently susceptible to noises, which adversely corrupt the information encoded in quantum systems. In this work, we introduce an efficient algorithm that can recover information from quantum states under Pauli noise. The core idea is to learn the necessary information of the unknown Pauli channel by post-processing the classical shadows of the channel. For a local and bounded-degree observable, only partial knowledge of the channel is required rather than its complete classical description to recover the ideal information, resulting in a polynomial-time algorithm. This contrasts with conventional methods such as probabilistic error cancellation, which requires the full information of the channel and exhibits exponential scaling with the number of qubits. We also prove that this scalable method is optimal on the sample complexity and generalise the algorithm to the weight contracting channel. Furthermore, we demonstrate the validity of the algorithm on the 1D anisotropic Heisenberg-type model via numerical simulations. As a notable application, our method can be severed as a sample-efficient error mitigation scheme for Clifford circuits.
@misc{CYZW23, title = {Efficient Information Recovery from {{Pauli}} Noise via Classical Shadow}, author = {Chen, Yifei and Yu, Zhan and Zhu, Chenghong and Wang, Xin}, year = {2023}, month = may, number = {arXiv:2305.04148}, primaryclass = {math-ph, physics:quant-ph}, publisher = {{arXiv}}, doi = {10.48550/arXiv.2305.04148}, url = {http://arxiv.org/abs/2305.04148}, archiveprefix = {arxiv}, }
Quantum Algorithms and Complexity
- On Estimating Operator Norm Distance, with Optimal Trace Distance Estimation When One State Is PureYupan Liu, Qisheng Wang, and Zhan Yu*Jul 2026Accepted as a talk at ESA 2026.
@misc{LWY26, title = {On Estimating Operator Norm Distance, with Optimal Trace Distance Estimation When One State Is Pure}, author = {Liu, Yupan and Wang, Qisheng and Yu, Zhan}, year = {2026}, month = jul, primaryclass = {quant-ph}, publisher = {arXiv}, url = {https://arxiv.org/abs/2607.03905}, note = {Accepted as a talk at ESA 2026.} } - Simultaneous Estimation of Nonlinear Functionals of a Quantum StateIEEE Transactions on Information Theory, Jun 2026Accepted as a regular talk at AQIS 2025.
@article{CWYZ26, title = {Simultaneous Estimation of Nonlinear Functionals of a Quantum State}, author = {Chen, Kean and Wang, Qisheng and Yu, Zhan and Zhang, Zhicheng}, year = {2026}, month = jun, journal = {IEEE Transactions on Information Theory}, publisher = {IEEE}, url = {https://ieeexplore.ieee.org/abstract/document/11551673}, note = {Accepted as a regular talk at AQIS 2025.} } - Quantum Phase Processing and Its Applications in Estimating Phase and EntropiesPhysical Review A, Dec 2023Accepted as a regular talk at AQIS 2023.
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts. Based on this unique principle of quantum computing, we develop a new algorithmic toolbox “quantum phase processing” that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled-unitaries, typically using only one ancilla qubit. Besides the capability of phase transformation, quantum phase processing in particular can extract the eigen-information of quantum systems by simply measuring the ancilla qubit, making it naturally compatible with indirect measurement. Quantum phase processing complements another powerful framework known as quantum singular value transformation and leads to more intuitive and efficient quantum algorithms for solving problems that are particularly phase-related. As a notable application, we propose a new quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far. We further exploit the power of our method by investigating a plethora of applications in Hamiltonian simulation, entanglement spectroscopy and quantum entropies estimation, demonstrating improvements or optimality for almost all cases.
@article{WZYW23, title = {Quantum Phase Processing and Its Applications in Estimating Phase and Entropies}, author = {Wang, Youle and Zhang, Lei and Yu, Zhan and Wang, Xin}, year = {2023}, month = dec, journal = {Physical Review A}, volume = {108}, number = {6}, pages = {062413}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.108.062413}, url = {https://link.aps.org/doi/10.1103/PhysRevA.108.062413}, note = {Accepted as a regular talk at AQIS 2023.} } - Analysis of Lackadaisical Quantum WalksPeter Høyer and Zhan Yu*Quantum Information and Computation, Nov 2020
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs. Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any locally arc-transitive graph.
@article{HY20, title = {Analysis of {{Lackadaisical Quantum Walks}}}, author = {H{\o}yer, Peter and Yu, Zhan}, year = {2020}, month = nov, journal = {Quantum Information and Computation}, volume = {20}, number = {13\&14}, primaryclass = {quant-ph}, pages = {1138--1153}, issn = {15337146, 15337146}, doi = {10.26421/QIC20.13-14-4}, url = {http://arxiv.org/abs/2002.11234}, }
Quantum Machine Learning
- A Gentle Introduction to Quantum Machine LearningYuxuan Du, Xinbiao Wang, Naixu Guo, Zhan Yu, Yang Qian, Kaining Zhang, Min-Hsiu Hsieh, Patrick Rebentrost, and Dacheng Tao2025
@book{DWG+25, title = {A Gentle Introduction to Quantum Machine Learning}, author = {Du, Yuxuan and Wang, Xinbiao and Guo, Naixu and Yu, Zhan and Qian, Yang and Zhang, Kaining and Hsieh, Min-Hsiu and Rebentrost, Patrick and Tao, Dacheng}, year = {2025}, publisher = {Springer Nature Singapore}, doi = {10.1007/978-981-95-1284-3}, isbn = {978-981-95-1283-6}, url = {https://link.springer.com/book/10.1007/978-981-95-1284-3}, } - Quantum Linear Algebra Is All You Need for Transformer ArchitecturesNaixu Guo, Zhan Yu, Matthew Choi, Aman Agrawal, Kouhei Nakaji, Alán Aspuru-Guzik, and Patrick RebentrostMay 2024
Generative machine learning methods such as large-language models are revolutionizing the creation of text and images. While these models are powerful they also harness a large amount of computational resources. The transformer is a key component in large language models that aims to generate a suitable completion of a given partial sequence. In this work, we investigate transformer architectures under the lens of fault-tolerant quantum computing. The input model is one where pre-trained weight matrices are given as block encodings to construct the query, key, and value matrices for the transformer. As a first step, we show how to prepare a block encoding of the self-attention matrix, with a row-wise application of the softmax function using the Hadamard product. In addition, we combine quantum subroutines to construct important building blocks in the transformer, the residual connection, layer normalization, and the feed-forward neural network. Our subroutines prepare an amplitude encoding of the transformer output, which can be measured to obtain a prediction. We discuss the potential and challenges for obtaining a quantum advantage.
@misc{GYC+24, title = {Quantum Linear Algebra Is All You Need for {{Transformer}} Architectures}, author = {Guo, Naixu and Yu, Zhan and Choi, Matthew and Agrawal, Aman and Nakaji, Kouhei and {Aspuru-Guzik}, Al{\'a}n and Rebentrost, Patrick}, year = {2024}, month = may, number = {arXiv:2402.16714}, primaryclass = {quant-ph}, publisher = {arXiv}, doi = {10.48550/arXiv.2402.16714}, url = {http://arxiv.org/abs/2402.16714}, archiveprefix = {arXiv}, } - Non-Asymptotic Approximation Error Bounds of Parameterized Quantum CircuitsIn Advances in Neural Information Processing Systems, Dec 2024
Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper investigates the expressivity of PQCs for approximating general multivariate function classes. Unlike previous Universal Approximation Theorems for PQCs, which are either nonconstructive or rely on parameterized classical data processing, we explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions. We establish the first non-asymptotic approximation error bounds for these functions in terms of the number of qubits, quantum circuit depth, and number of trainable parameters. Notably, we demonstrate that for approximating functions that satisfy specific smoothness criteria, the quantum circuit size and number of trainable parameters of our proposed PQCs can be smaller than those of deep ReLU neural networks. We further validate the approximation capability of PQCs through numerical experiments. Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.
@inproceedings{YCJ+24, title = {Non-Asymptotic {{Approximation Error Bounds}} of {{Parameterized Quantum Circuits}}}, author = {Yu, Zhan and Chen, Qiuhao and Jiao, Yuling and Li, Yinan and Lu, Xiliang and Wang, Xin and Yang, Jerry Zhijian}, year = {2024}, month = dec, booktitle = {Advances in Neural Information Processing Systems}, volume = {37}, publisher = {{Curran Associates, Inc.}}, primaryclass = {quant-ph}, doi = {10.52202/079017-3143}, url = {https://proceedings.neurips.cc/paper_files/paper/2024/hash/b360fd42ced877429882a2a68b4a4343-Abstract-Conference.html}, } - Power and Limitations of Single-Qubit Native Quantum Neural NetworksZhan Yu, Hongshun Yao, Mujin Li, and Xin WangIn Advances in Neural Information Processing Systems, 2022
Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. Beyond previous works’ understanding of existence, we in particular establish the exact correlations between the parameters of the trainable gates and the working Fourier coefficients, by exploring connections to quantum signal processing. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. As applications, we introduce natural extensions to multi-qubit quantum neural networks, which exhibit the capability of classifying real-world multi-dimensional data. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.
@inproceedings{YYLW22, title = {Power and Limitations of Single-Qubit Native Quantum Neural Networks}, booktitle = {Advances in Neural Information Processing Systems}, author = {Yu, Zhan and Yao, Hongshun and Li, Mujin and Wang, Xin}, editor = {Koyejo, S. and Mohamed, S. and Agarwal, A. and Belgrave, D. and Cho, K. and Oh, A.}, year = {2022}, volume = {35}, pages = {27810--27823}, publisher = {{Curran Associates, Inc.}}, url = {https://proceedings.neurips.cc/paper_files/paper/2022/file/b250de41980b58d34d6aadc3f4aedd4c-Paper-Conference.pdf}, } - Optimal Quantum Dataset for Learning a Unitary TransformationPhysical Review Applied, Mar 2023
Unitary transformations formulate the time evolution of quantum states. How to learn a unitary transformation efficiently is a fundamental problem in quantum machine learning. The most natural and leading strategy is to train a quantum machine learning model based on a quantum dataset. Although the presence of more training data results in better models, using too much data reduces the efficiency of training. In this work, we solve the problem on the minimum size of sufficient quantum datasets for learning a unitary transformation exactly, which reveals the power and limitation of quantum data. First, we prove that the minimum size of a dataset with pure states is 2n for learning an n-qubit unitary transformation. To fully explore the capability of quantum data, we introduce a practical quantum dataset consisting of n+1 elementary tensor product states that are sufficient for exact training. The main idea is to simplify the structure utilizing decoupling, which leads to an exponential improvement in the size of the datasets with pure states. Furthermore, we show that the size of the quantum dataset with mixed states can be reduced to a constant, which yields an optimal quantum dataset for learning a unitary. We showcase the applications of our results in oracle compiling and Hamiltonian simulation. Notably, to accurately simulate a three-qubit one-dimensional nearest-neighbor Heisenberg model, our circuit only uses 96 elementary quantum gates, which is significantly less than 4080 gates in the circuit constructed by the Trotter-Suzuki product formula.
@article{YZZW23, title = {Optimal {{Quantum Dataset}} for {{Learning}} a {{Unitary Transformation}}}, author = {Yu, Zhan and Zhao, Xuanqiang and Zhao, Benchi and Wang, Xin}, year = {2023}, month = mar, journal = {Physical Review Applied}, volume = {19}, number = {3}, pages = {034017}, publisher = {{American Physical Society}}, doi = {10.1103/PhysRevApplied.19.034017}, url = {https://link.aps.org/doi/10.1103/PhysRevApplied.19.034017}, }