Hamiltonian Simulation by Qubitization

Guang Hao Low; Isaac L. Chuang

doi:10.22331/q-2019-07-12-163

Hamiltonian Simulation by Qubitization

Guang Hao Low¹ and Isaac L. Chuang²

¹Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
²Department of Electrical Engineering and Computer Science, Department of Physics, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Published:	2019-07-12, volume 3, page 163
Eprint:	arXiv:1610.06546v3
Doi:	https://doi.org/10.22331/q-2019-07-12-163
Citation:	Quantum 3, 163 (2019).

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Abstract

We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a unitary oracle $\hat{U}$ onto the state $|G\rangle$ created by another unitary oracle. Our algorithm solves this with a query complexity $\mathcal{O}\big(t+\log({1/\epsilon})\big)$ to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are $d$-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where $\hat{H}$ is a density matrix. A key technical result is `qubitization', which uses the controlled version of these oracles to embed any $\hat{H}$ in an invariant $\text{SU}(2)$ subspace. A large class of operator functions of $\hat{H}$ can then be computed with optimal query complexity, of which $e^{-i\hat{H}t}$ is a special case.

► BibTeX data

@article{Low2019hamiltonian,
  doi = {10.22331/q-2019-07-12-163},
  url = {https://doi.org/10.22331/q-2019-07-12-163},
  title = {Hamiltonian {S}imulation by {Q}ubitization},
  author = {Low, Guang Hao and Chuang, Isaac L.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {163},
  month = jul,
  year = {2019}
}

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[62] Kouhei Nakaji, Mohsen Bagherimehrab, and Alán Aspuru-Guzik, "High-Order Randomized Compiler for Hamiltonian Simulation", PRX Quantum 5 2, 020330 (2024).

[63] Cristian L. Cortes, Dario Rocca, Jérôme F. Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Assessing the query complexity limits of quantum phase estimation using symmetry-aware spectral bounds", Physical Review A 110 2, 022420 (2024).

[64] Angus Kan, Jessica Lemieux, Olga Okrut, and Burak Şahinoğlu, "Optimized quantum algorithms for simulating the Schwinger effect", Physical Review D 113 11, 114503 (2026).

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[66] Qi Zhao, You Zhou, and Andrew M. Childs, "Entanglement accelerates quantum simulation", Nature Physics 21 8, 1338 (2025).

[67] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Lattice renormalization of quantum simulations", Physical Review D 104 9, 094519 (2021).

[68] Yonah Borns-Weil, Di Fang, and Jiaqi Zhang, "Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation", Communications in Mathematical Physics 407 2, 29 (2026).

[69] Angus Kan and Benjamin C. B. Symons, "Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model and high-temperature superconductor models", npj Quantum Information 11 1, 138 (2025).

[70] Vibin Abraham, Priyabrata Senapati, Himadri Pathak, and Bo Peng, "Elucidating many-body effects in molecular core spectra through real-time approaches: Efficient classical approximations and a quantum perspective", The Journal of Chemical Physics 164 10, 104113 (2026).

[71] Muhammad Asaduzzaman, Raghav G. Jha, and Bharath Sambasivam, "Sachdev-Ye-Kitaev model on a noisy quantum computer", Physical Review D 109 10, 105002 (2024).

[72] Andrew M. Childs, Aaron Ostrander, and Yuan Su, "Faster quantum simulation by randomization", Quantum 3, 182 (2019).

[73] Bin Cheng, Xiu-Hao Deng, Xiu Gu, Yu He, Guangchong Hu, Peihao Huang, Jun Li, Ben-Chuan Lin, Dawei Lu, Yao Lu, Chudan Qiu, Hui Wang, Tao Xin, Shi Yu, Man-Hong Yung, Junkai Zeng, Song Zhang, Youpeng Zhong, Xinhua Peng, Franco Nori, and Dapeng Yu, "Noisy intermediate-scale quantum computers", Frontiers of Physics 18 2, 21308 (2023).

[74] Zane M. Rossi and Isaac L. Chuang, "Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle", Quantum 6, 811 (2022).

[75] Chusei Kiumi and Bálint Koczor, "TE-PAI: exact time evolution by sampling random circuits", Quantum Science and Technology 10 4, 045071 (2025).

[76] Nhat A. Nghiem, Xianfeng David Gu, and Tzu-Chieh Wei, "Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach", Quantum 9, 1955 (2025).

[77] Jessica Lemieux, Guillaume Duclos-Cianci, David Sénéchal, and David Poulin, "Resource estimate for quantum many-body ground-state preparation on a quantum computer", Physical Review A 103 5, 052408 (2021).

[78] Boyang Chen, Jue Xu, Xiao Yuan, and Qi Zhao, "General Framework for Error Interference in Quantum Simulation", Physical Review Letters 136 20, 200601 (2026).

[79] Abeynaya Gnanasekaran and Amit Surana, "Efficient quantum access model for sparse structured matrices using linear combination of “things”", Physical Review A 113 2, 022437 (2026).

[80] Paul K. Faehrmann, Mark Steudtner, Richard Kueng, Maria Kieferova, and Jens Eisert, "Randomizing multi-product formulas for Hamiltonian simulation", Quantum 6, 806 (2022).

[81] Xue-Jia Yu, Limei Xu, and Hai-Qing Lin, "Topological physics in quantum critical systems", Physics Reports 1160, 1 (2026).

[82] Qian Xu, Hengyun Zhou, Guo Zheng, Dolev Bluvstein, J. Pablo Bonilla Ataides, Mikhail D. Lukin, and Liang Jiang, "Fast and Parallelizable Logical Computation with Homological Product Codes", Physical Review X 15 2, 021065 (2025).

[83] Javier Gonzalez-Conde, Ángel Rodríguez-Rozas, Enrique Solano, and Mikel Sanz, "Efficient Hamiltonian simulation for solving option price dynamics", Physical Review Research 5 4, 043220 (2023).

[84] Mostafizur Rahaman Laskar and Amit Kumar Dutta, "A Complexity-Efficient Quantum Architecture and Simulation for Eigen Spectrum Estimation of Vandermonde System in a Large Antenna Array", IEEE Transactions on Circuits and Systems I: Regular Papers 70 5, 2106 (2023).

[85] Lei Zhang, Jizhe Lai, Xian Wu, and Xin Wang, "Quantum imaginary-time evolution with polynomial resources in evolution time", Quantum Science and Technology 11 3, 035041 (2026).

[86] Tatiana A. Bespalova and Oleksandr Kyriienko, "Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation", PRX Quantum 2 3, 030318 (2021).

[87] Luca Spagnoli, Chiara Lissoni, and Alessandro Roggero, "Quantum Simulation of Nuclear Dynamics in First Quantization", Quantum 10, 2200 (2026).

[88] Andrés Gómez and Javier Mas, "Hermitian matrix definiteness from quantum phase estimation", Quantum Information Processing 21 6, 213 (2022).

[89] Matthew L. Goh and Bálint Koczor, "Direct estimation of the density of states for fermionic systems", Physical Review Research 8 1, 013250 (2026).

[90] S M Abdullah Al Mamun, Shuangbao Wang, John Joseph Kath, Daniel O’Malley, Qinjun Kang, and Zheng Li, "Quantum unitary lattice Boltzmann formulation for canonical flow and thermal transport simulation", Journal of Computational Physics 568, 115381 (2027).

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[92] Jing 静 Li 李, Yanqi 燕琪 Song 宋, Sujuan 素娟 Qin 秦, Wenmin 文敏 Li 李, and Fei 飞 Gao 高, "Quantum algorithm for marginal Fisher analysis", Chinese Physics B 34 12, 120302 (2025).

[93] Pedro C.S. Costa, Dong An, Yuval R. Sanders, Yuan Su, Ryan Babbush, and Dominic W. Berry, "Optimal Scaling Quantum Linear-Systems Solver via Discrete Adiabatic Theorem", PRX Quantum 3 4, 040303 (2022).

[94] Yingbin Chen and Shaoping Xiao, "A simulator-based quantum framework for molecular dynamics and multiscale materials modeling", Academia Quantum 3 3(2026).

[95] Dominic W. Berry, Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush, "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization", Quantum 3, 208 (2019).

[96] Margarite L. LaBorde and Mark M. Wilde, "Quantum Algorithms for Testing Hamiltonian Symmetry", Physical Review Letters 129 16, 160503 (2022).

[97] Arnab Adhikary, S E Skelton, Alberto Nocera, and Mona Berciu, "Advantage of warm starts for electron–phonon systems on quantum computers", Quantum Science and Technology 11 4, 045065 (2026).

[98] Yukuan Tao, Mădălin Guţă, and Gerardo Adesso, "Trade-off Between Complexity and Energy in Quantum Phase Estimation", PRX Energy 5 3, 033016 (2026).

[99] Shang Gao and Yu-Guang Yang, "A novel quantum recommender system", Physica Scripta 98 1, 010001 (2023).

[100] Olivia Di Matteo, Anna McCoy, Peter Gysbers, Takayuki Miyagi, R. M. Woloshyn, and Petr Navrátil, "Improving Hamiltonian encodings with the Gray code", Physical Review A 103 4, 042405 (2021).

[101] Pauline J. Ollitrault, Jérôme F. Gonthier, Dario Rocca, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Improving the Runtime of Quantum Phase Estimation for Chemistry through Basis Set Optimization", Journal of Chemical Theory and Computation 21 23, 12034 (2025).

[102] Soumita Naskar, Mostafizur Rahaman Laskar, and Amit Kumar Dutta, "QRadCom: Quantum-Assisted Source and Symbol Detection Framework in a Radar Communication System With Low-Computational Complexity", IEEE Transactions on Cognitive Communications and Networking 12, 912 (2026).

[103] Erik J. Gustafson, Henry Lamm, Felicity Lovelace, and Damian Musk, "Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral", Physical Review D 106 11, 114501 (2022).

[104] Petr Ivashkov, Po-Wei Huang, Kelvin Koor, Lirandë Pira, and Patrick Rebentrost, "QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation", npj Quantum Information 12 1, 73 (2026).

[105] William Kirby, Bryce Fuller, Charles Hadfield, and Antonio Mezzacapo, "Second-Quantized Fermionic Operators with Polylogarithmic Qubit and Gate Complexity", PRX Quantum 3 2, 020351 (2022).

[106] Kaito Mizukami and Akihisa Koga, "Quantum algorithm for the microcanonical thermal pure quantum state method", Physical Review A 108 1, 012404 (2023).

[107] Sapthagiri Miriyala and Venkata Ramireddy Chirra, "From Quantum Algorithm Primitives to Design Patterns: A Unified Framework for NISQ and Fault‐Tolerant Regimes", Advanced Quantum Technologies 9 6, e70310 (2026).

[108] Smik Patel, Aritra Sankar Brahmachari, Joshua T. Cantin, Linjun Wang, and Artur F. Izmaylov, "Global Minimization of Electronic Hamiltonian 1-Norm via Linear Programming in the Block Invariant Symmetry Shift (BLISS) Method", Journal of Chemical Theory and Computation 21 2, 703 (2025).

[109] Noah Brustle and Nathan Wiebe, "Quantum and classical algorithms for nonlinear unitary dynamics", Quantum 9, 1741 (2025).

[110] Lorenzo Laneve, "An adversary bound for quantum signal processing", Quantum 10, 2025 (2026).

[111] Carlos A. Riofrío, Johannes Klepsch, Jernej Rudi Finžgar, Florian Kiwit, Leonhard Hölscher, Marvin Erdmann, Lukas Müller, Chandan Kumar, Youssef Achari Berrada, and Andre Luckow, Quantum Computational AI 181 (2026) ISBN:9780443302596.

[112] Youle Wang, "Near-optimal quantum kernel principal component analysis", Quantum Science and Technology 10 1, 015034 (2025).

[113] Wenjun Yu, Jinzhao Sun, Zeyao Han, and Xiao Yuan, "Robust and Efficient Hamiltonian Learning", Quantum 7, 1045 (2023).

[114] Zhicheng Zhang, Qisheng Wang, and Mingsheng Ying, "Parallel Quantum Algorithm for Hamiltonian Simulation", Quantum 8, 1228 (2024).

[115] Daniel Volya and Prabhat Mishra, "State Preparation on Quantum Computers via Quantum Steering", IEEE Transactions on Quantum Engineering 5, 1 (2024).

[116] Earl T Campbell, "Early fault-tolerant simulations of the Hubbard model", Quantum Science and Technology 7 1, 015007 (2022).

[117] James D. Watson and Jacob Watkins, "Exponentially Reduced Circuit Depths Using Trotter Error Mitigation", PRX Quantum 6 3, 030325 (2025).

[118] Pau Escofet, Alejandro Gonzalvo, Eduard Alarcón, Carmen G. Almudéver, and Sergi Abadal, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 909 (2024) ISBN:979-8-3315-4137-8.

[119] Xiao-Ming Zhang, Yukun Zhang, Wenhao He, and Xiao Yuan, "Exponential Quantum Advantages for Practical Non-Hermitian Eigenproblems", Physical Review Letters 135 14, 140601 (2025).

[120] Chuwen Ma, Shi Jin, Nana Liu, Kezhen Wang, and Lei Zhang, "Schrödingerization-Based Quantum Circuits For Maxwell’s Equations With Time-Dependent Source Terms", Journal of Scientific Computing 108 2, 43 (2026).

[121] Zongping Gong and Ryusuke Hamazaki, "Bounds in nonequilibrium quantum dynamics", International Journal of Modern Physics B 36 31, 2230007 (2022).

[122] Yu Cao, Shi Jin, and Nana Liu, "Quantum simulation for time-dependent Hamiltonians—with applications to non-autonomous ordinary and partial differential equations", Journal of Physics A: Mathematical and Theoretical 58 15, 155304 (2025).

[123] Etienne Granet and Henrik Dreyer, "Dilution of Error in Digital Hamiltonian Simulation", PRX Quantum 6 1, 010333 (2025).

[124] Francoise Golse, Shi Jin, and Nana Liu, "Quantum algorithms for uncertainty quantification: Applications to partial differential equations", Science China Physics, Mechanics & Astronomy 68 10, 104704 (2025).

[125] Nhat A. Nghiem and Tzu-Chieh Wei, "Improved quantum algorithms for eigenvalue finding and gradient descent", Physical Review Applied 25 5, 054024 (2026).

[126] Xiu Gu, Jorge Fernández-Pendás, Pontus Vikstål, Tahereh Abad, Christopher Warren, Andreas Bengtsson, Giovanna Tancredi, Vitaly Shumeiko, Jonas Bylander, Göran Johansson, and Anton Frisk Kockum, "Fast Multiqubit Gates through Simultaneous Two-Qubit Gates", PRX Quantum 2 4, 040348 (2021).

[127] Dorota M. Grabowska, Christopher F. Kane, and Christian W. Bauer, "Fully gauge-fixed SU(2) Hamiltonian for quantum simulations", Physical Review D 111 11, 114516 (2025).

[128] Jia-Cheng Huang, Hao-En Li, Yi-Cheng Wang, Guang-Ze Zhang, Jun Li, and Han-Shi Hu, "Towards Robust Variational Quantum Simulation of Lindblad Dynamics via Stochastic Magnus Expansion", PRX Quantum 6 4, 040312 (2025).

[129] Yulong Dong, Xiang Meng, K. Birgitta Whaley, and Lin Lin, "Efficient phase-factor evaluation in quantum signal processing", Physical Review A 103 4, 042419 (2021).

[130] César Feniou, Christopher Cherfan, Julien Zylberman, Baptiste Claudon, Jean-Philip Piquemal, and Emmanuel Giner, "Real-space chemistry on quantum computers: a fault-tolerant algorithm with adaptive grids and a transcorrelated extension", Digital Discovery (2026).

[131] Maria Tudorovskaya and David Muñoz Ramo, "Quantum computing simulation of a mixed spin-boson Hamiltonian and its performance for a cavity quantum electrodynamics problem", Physical Review A 109 3, 032612 (2024).

[132] John S. Van Dyke, George S. Barron, Nicholas J. Mayhall, Edwin Barnes, and Sophia E. Economou, "Preparing Bethe Ansatz Eigenstates on a Quantum Computer", PRX Quantum 2 4, 040329 (2021).

[133] Timothy Stroschein, Davide Castaldo, and Markus Reiher, "Ground- and excited-state energies with analytic errors and short time evolution on a quantum computer", Physical Review Research 8 3, 033177 (2026).

[134] Shalev Ben-David, Andrew M. Childs, András Gilyén, William Kretschmer, Supartha Podder, and Daochen Wang, "Symmetries, Graph Properties, and Quantum Speedups", SIAM Journal on Computing 53 6, FOCS20-368 (2024).

[135] Dominic W. Berry, Kianna Wan, Andrew D. Baczewski, Elliot C. Eklund, Arkin Tikku, and Ryan Babbush, "Quantum Simulation of Electronic Structure via Quantum Fast Multipole Method", PRX Quantum 7 3, 033025 (2026).

[136] Nicolas PD Sawaya, Albert T Schmitz, and Stuart Hadfield, "Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems", Quantum 7, 1111 (2023).

[137] Marcin Kotowski, Michał Oszmaniec, and Michał Horodecki, "Extremal jumps of circuit complexity of unitary evolutions generated by random Hamiltonians", Journal of High Energy Physics 2025 1, 116 (2025).

[138] Nhat A. Nghiem and Tzu-Chieh Wei, "Quantum algorithm for solving nonlinear algebraic equations", Physical Review Applied 24 5, 054005 (2025).

[139] Srikar Chundury, Blake Burgstahler, Jiajia Li, In-Saeng Suh, and Frank Mueller, Proceedings of the 40th ACM International Conference on Supercomputing 1350 (2026) ISBN:9798400725227.

[140] Sven Danz, Mario Berta, Stefan Schröder, Pascal Kienast, Frank K. Wilhelm, and Alessandro Ciani, "Calculating response functions of coupled oscillators using quantum phase estimation", Physical Review Research 7 2, 023264 (2025).

[141] Nhat A. Nghiem and Tzu-Chieh Wei, "Hybrid quantum-classical framework for Betti-number estimation with applications to topological data analysis", Physical Review A 114 4, 042443 (2026).

[142] Masahito Hayashi and Yuxiang Yang, "Efficient algorithms for quantum information bottleneck", Quantum 7, 936 (2023).

[143] Naixu Guo, Kosuke Mitarai, and Keisuke Fujii, "Nonlinear transformation of complex amplitudes via quantum singular value transformation", Physical Review Research 6 4, 043227 (2024).

[144] Duarte Magano, João Moutinho, and Bruno Coutinho, "On the quantum simulation of complex networks", SciPost Physics Core 6 3, 058 (2023).

[145] Chuqing Wang, Hefeng Wang, and Hua Xiang, "Quantum algorithm for PageRank computation through multistep quantum resonant transitions", Journal of Computational and Applied Mathematics 491, 118059 (2027).

[146] Fuchuan Wei, Zhenhuan Liu, Guoding Liu, Zizhao Han, Dong-Ling Deng, and Zhengwei Liu, "Simulating non-completely positive actions via exponentiation of Hermitian-preserving maps", npj Quantum Information 10 1, 134 (2024).

[147] András Gilyén, Seth Lloyd, Iman Marvian, Yihui Quek, and Mark M. Wilde, "Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements", Physical Review Letters 128 22, 220502 (2022).

[148] Xuefen Zhang and Chuangtao Chen, "Unitary dilation based coherent realization of nonnormal measurement blocks in quantum weighted state algorithms", Future Generation Computer Systems 188, 108829 (2027).

[149] Linpan Jiang, Xiao Geng, Genting Dai, Kaiyong He, Mingjun Cheng, Liangliang Yang, Jinlin Chang, Jianshe Liu, and Wei Chen, "A quantum-imaginary-time-evolution-based simulation of parallel mutation-selection-drift model", Physics Letters A 591, 131896 (2026).

[150] Zihao Liu, Guanzhong Li, and Lvzhou Li, "Improved quantum linear system solver via quantum phase discrimination", The European Physical Journal Special Topics 234 20, 6241 (2025).

[151] Qisheng Wang, Zhicheng Zhang, Kean Chen, Ji Guan, Wang Fang, Junyi Liu, and Mingsheng Ying, "Quantum Algorithm for Fidelity Estimation", IEEE Transactions on Information Theory 69 1, 273 (2023).

[152] Yuta Kikuchi, Conor Mc Keever, Luuk Coopmans, Michael Lubasch, and Marcello Benedetti, "Realization of quantum signal processing on a noisy quantum computer", npj Quantum Information 9 1, 93 (2023).

[153] Joonsuk Huh, "Quantum estimation bound of the Gaussian matrix permanent", Physical Review A 111 1, 012418 (2025).

[154] Andrew K. Tan, Yuan Liu, Minh C. Tran, and Isaac L. Chuang, "Perturbative model of noisy quantum signal processing", Physical Review A 107 4, 042429 (2023).

[155] Chengkai Zhu, Shuyu He, Yu-Ao Chen, Lei Zhang, and Xin Wang, "Optimal Hamiltonian recognition of unknown quantum dynamics", npj Quantum Information 12 1, 36 (2026).

[156] P A M Casares and M A Martin-Delgado, "A quantum interior-point predictor–corrector algorithm for linear programming", Journal of Physics A: Mathematical and Theoretical 53 44, 445305 (2020).

[157] Cyrill Bösch, Malte Schade, Giacomo Aloisi, Scott D. Keating, and Andreas Fichtner, "Quantum wave simulation with sources and loss functions", Physical Review Research 7 3, 033225 (2025).

[158] Chukwudubem Umeano, Stefano Scali, and Oleksandr Kyriienko, "Quantum community detection via deterministic elimination", Physical Review A 112 5, 052422 (2025).

[159] Hefeng Wang and Sixia Yu, "Quantum algorithm for preparing the ground state of a physical system through multi-step quantum resonant transitions", Quantum Information Processing 20 1, 40 (2021).

[160] Myeongjin Shin, Junseo Lee, and Changhun Oh, "Heisenberg-Limited Hamiltonian Learning Without Short-Time Control", PRX Quantum 7 4, 043011 (2026).

[161] Yiran 怡冉 Bai 白, Feng 枫 Xiong 熊, and Xueheng 学衡 Kuang 匡, "Random State Approach to Quantum Computation of Electronic-Structure Properties", Chinese Physics Letters 43 1, 010604 (2025).

[162] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", Reviews of Modern Physics 92 1, 015003 (2020).

[163] Koichi Miyamoto, Soichiro Yamazaki, Fumio Uchida, Kotaro Fujisawa, and Naoki Yoshida, "Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos", Physical Review Research 6 1, 013200 (2024).

[164] Jeongwan Haah, "Product Decomposition of Periodic Functions in Quantum Signal Processing", Quantum 3, 190 (2019).

[165] Seenivasan Hariharan, Sachin Kinge, and Lucas Visscher, "Modeling Heterogeneous Catalysis Using Quantum Computers: An Academic and Industry Perspective", Journal of Chemical Information and Modeling 65 2, 472 (2025).

[166] Hengyun Zhou, Casey Duckering, Chen Zhao, Dolev Bluvstein, Madelyn Cain, Aleksander Kubica, Sheng-Tao Wang, and Mikhail D. Lukin, Proceedings of the 52nd Annual International Symposium on Computer Architecture 1432 (2025) ISBN:9798400712616.

[167] L. Spagnoli, A. Roggero, and N. Wiebe, "Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes", Quantum 10, 1968 (2026).

[168] Guillermo Alonso-Linaje, Utkarsh Azad, Jay Soni, Jarrett Smalley, Leigh Lapworth, and Juan Miguel Arrazola, "Quantum compilation framework for data loading", Quantum Science and Technology 11 4, 045092 (2026).

[169] I-Chi Chen, João C. Getelina, Klée Pollock, Aleksei Khindanov, Srimoyee Sen, Yong-Xin Yao, and Thomas Iadecola, "Classical and quantum simulations of 1+1-dimensional $${{\mathbb{Z}}}_{2}$$ gauge theory at finite temperature and density", Communications Physics 8 1, 375 (2025).

[170] Sam McArdle, Earl Campbell, and Yuan Su, "Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian", Physical Review A 105 1, 012403 (2022).

[171] Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics", Nature Computational Science 3 1, 25 (2022).

[172] Zhong-Xia Shang, Naixu Guo, Dong An, and Qi Zhao, "Designing a Nearly Optimal Quantum Algorithm for Linear Differential Equations via Lindbladians", Physical Review Letters 135 12, 120604 (2025).

[173] Amirhossein Lame Jouybari and Leon Cizelj, "Prospect of quantum computing on Enhanced Strain Gradient Crystal Plasticity theory", International Journal of Plasticity 202, 104711 (2026).

[174] Liming YANG, Yang XIAO, Chang SHU, and Yinjie DU, "Quantum Taylor series expansion and least squares-based fractional-step LBM for incompressible flows on non-uniform meshes", Chinese Journal of Aeronautics 39 6, 104176 (2026).

[175] J. E. Elenewski, C. M. Camara, and A. Kalev, "Prospects for NMR spectral prediction on fault-tolerant quantum computers", Physical Review Research 8 1, 013315 (2026).

[176] Aleksei V. Ivanov, Andrew Patterson, Marius Bothe, Christoph Sünderhauf, Bjorn K. Berntson, Jens Jørgen Mortensen, Mikael Kuisma, Earl Campbell, and Róbert Izsák, "Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set", Journal of Chemical Theory and Computation 21 15, 7360 (2025).

[177] Trevor Keen, Thomas Maier, Steven Johnston, and Pavel Lougovski, "Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware", Quantum Science and Technology 5 3, 035001 (2020).

[178] Matteo Capone, Marco Romanelli, Davide Castaldo, Giovanni Parolin, Alessandro Bello, Gabriel Gil, and Mirko Vanzan, "A Vision for the Future of Multiscale Modeling", ACS Physical Chemistry Au 4 3, 202 (2024).

[179] Samson Wang, Sam McArdle, and Mario Berta, "Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra", PRX Quantum 5 2, 020324 (2024).

[180] Jordan Cioni and Fabio Semperlotti, "Spectral quantum algorithm for numerical differentiation and integration", Physical Review Applied 26 1, 014063 (2026).

[181] Leonardo Lavagna, Sandra Carillo, and Massimo Panella, "A topical review on time-independent perturbation theory in one-dimensional quantum systems", Physica Scripta 100 10, 102001 (2025).

[182] Yuri Alexeev, Maximilian Amsler, Marco Antonio Barroca, Sanzio Bassini, Torey Battelle, Daan Camps, David Casanova, Young Jay Choi, Frederic T. Chong, Charles Chung, Christopher Codella, Antonio D. Córcoles, James Cruise, Alberto Di Meglio, Ivan Duran, Thomas Eckl, Sophia Economou, Stephan Eidenbenz, Bruce Elmegreen, Clyde Fare, Ismael Faro, Cristina Sanz Fernández, Rodrigo Neumann Barros Ferreira, Keisuke Fuji, Bryce Fuller, Laura Gagliardi, Giulia Galli, Jennifer R. Glick, Isacco Gobbi, Pranav Gokhale, Salvador de la Puente Gonzalez, Johannes Greiner, Bill Gropp, Michele Grossi, Emanuel Gull, Burns Healy, Matthew R. Hermes, Benchen Huang, Travis S. Humble, Nobuyasu Ito, Artur F. Izmaylov, Ali Javadi-Abhari, Douglas Jennewein, Shantenu Jha, Liang Jiang, Barbara Jones, Wibe Albert de Jong, Petar Jurcevic, William Kirby, Stefan Kister, Masahiro Kitagawa, Joel Klassen, Katherine Klymko, Kwangwon Koh, Masaaki Kondo, Dog̃a Murat Kürkçüog̃lu, Krzysztof Kurowski, Teodoro Laino, Ryan Landfield, Matt Leininger, Vicente Leyton-Ortega, Ang Li, Meifeng Lin, Junyu Liu, Nicolas Lorente, Andre Luckow, Simon Martiel, Francisco Martin-Fernandez, Margaret Martonosi, Claire Marvinney, Arcesio Castaneda Medina, Dirk Merten, Antonio Mezzacapo, Kristel Michielsen, Abhishek Mitra, Tushar Mittal, Kyungsun Moon, Joel Moore, Sarah Mostame, Mario Motta, Young-Hye Na, Yunseong Nam, Prineha Narang, Yu-ya Ohnishi, Daniele Ottaviani, Matthew Otten, Scott Pakin, Vincent R. Pascuzzi, Edwin Pednault, Tomasz Piontek, Jed Pitera, Patrick Rall, Gokul Subramanian Ravi, Niall Robertson, Matteo A.C. Rossi, Piotr Rydlichowski, Hoon Ryu, Georgy Samsonidze, Mitsuhisa Sato, Nishant Saurabh, Vidushi Sharma, Kunal Sharma, Soyoung Shin, George Slessman, Mathias Steiner, Iskandar Sitdikov, In-Saeng Suh, Eric D. Switzer, Wei Tang, Joel Thompson, Synge Todo, Minh C. Tran, Dimitar Trenev, Christian Trott, Huan-Hsin Tseng, Norm M. Tubman, Esin Tureci, David García Valiñas, Sofia Vallecorsa, Christopher Wever, Konrad Wojciechowski, Xiaodi Wu, Shinjae Yoo, Nobuyuki Yoshioka, Victor Wen-zhe Yu, Seiji Yunoki, Sergiy Zhuk, and Dmitry Zubarev, "Quantum-centric supercomputing for materials science: A perspective on challenges and future directions", Future Generation Computer Systems 160, 666 (2024).

[183] Pablo Rodriguez-Grasa, Ruben Ibarrondo, Javier Gonzalez-Conde, Yue Ban, Patrick Rebentrost, and Mikel Sanz, "Quantum approximated cloning-assisted density matrix exponentiation", Physical Review Research 7 1, 013264 (2025).

[184] Christopher Kang and Yuan Su, "Quantum Matrix Arithmetics with Hamiltonian Evolution", ACM Transactions on Quantum Computing 7 4, 1 (2026).

[185] Nhat A. Nghiem, "Efficient quantum algorithm for simulating a time-dependent Hamiltonian that commutes at different times", Physical Review A 112 4, 042603 (2025).

[186] Konrad Deka and Emil Zak, "Simultaneously Optimizing Symmetry Shifts and Tensor Factorizations for Cost-Efficient Fault-Tolerant Quantum Simulations of Electronic Hamiltonians", Journal of Chemical Theory and Computation 21 9, 4458 (2025).

[187] Rodrigo Martinez Sanz, Andreu Angles-Castillo, Eduard Alarcon, and Carmen G. Almudever, "Efficiently Architecting VQAs: Expressibility–Trainability–Resources Pareto-Optimality", IEEE Transactions on Quantum Engineering 7, 3104517 (2026).

[188] Changhao Yi and Elizabeth Crosson, "Spectral analysis of product formulas for quantum simulation", npj Quantum Information 8 1, 37 (2022).

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[190] Marek Gluza, "Double-bracket quantum algorithms for diagonalization", Quantum 8, 1316 (2024).

[191] Christoph Sünderhauf, Earl Campbell, and Joan Camps, "Block-encoding structured matrices for data input in quantum computing", Quantum 8, 1226 (2024).

[192] Feng Zhang, Niladri Gomes, Joshua Aftergood, Thomas Iadecola, Yong‐Xin Yao, and Peter P. Orth, "Sampling Noise and Optimized Measurement Distribution in Imaginary‐Time Quantum Dynamics Simulations", Advanced Quantum Technologies 9 9, e70418 (2026).

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[194] Mario Motta, Erika Ye, Jarrod R. McClean, Zhendong Li, Austin J. Minnich, Ryan Babbush, and Garnet Kin-Lic Chan, "Low rank representations for quantum simulation of electronic structure", npj Quantum Information 7 1, 83 (2021).

[195] Luning Zhao, Qingfeng Wang, Joshua J. Goings, Kyujin Shin, Woomin Kyoung, Seunghyo Noh, Young Min Rhee, and Kyungmin Kim, "Enhancing the electron pair approximation with measurements on trapped-ion quantum computers", npj Quantum Information 10 1, 76 (2024).

[196] Ayse Kotil, Rahul Banerjee, Qunsheng Huang, and Christian B Mendl, "Riemannian quantum circuit optimization for Hamiltonian simulation", Journal of Physics A: Mathematical and Theoretical 57 13, 135303 (2024).

[197] Ljubomir Budinski, "Quantum algorithm for the advection–diffusion equation simulated with the lattice Boltzmann method", Quantum Information Processing 20 2, 57 (2021).

[198] Lei Cheng, Pan Gao, Tiejun Wang, and Keren Li, "Polynomial optimization with linear combination of unitaries", Physical Review A 109 3, 032429 (2024).

[199] Shantanav Chakraborty, "Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers", Quantum 8, 1496 (2024).

[200] Tong Ning, Youlong Yang, and Zhenye Du, "Quantum kernel logistic regression based Newton method", Physica A: Statistical Mechanics and its Applications 611, 128454 (2023).

[201] Yuuki Tokunaga, "Toward Early Fault-tolerant Quantum Computing", NTT Technical Review 21 11, 43 (2023).

[202] Lorenzo Laneve and Stefan Wolf, "On multivariate polynomials achievable with quantum signal processing", Quantum 9, 1641 (2025).

[203] Takumi Kobori, Taichi Kosugi, Hirofumi Nishi, Synge Todo, and Yu-ichiro Matsushita, "Accelerated spin-adapted ground-state preparation with nonvariational quantum algorithms", Physical Review A 113 6, 062454 (2026).

[204] Hongshun Yao, Yu-Ao Chen, Erdong Huang, Kaichu Chen, Honghao Fu, and Xin Wang, "Protocols and trade-offs of quantum state purification", Quantum Science and Technology 10 3, 035020 (2025).

[205] Erenay Karacan, Conor Mc Keever, Michael Foss-Feig, David Hayes, and Michael Lubasch, "Filter-enhanced adiabatic quantum computing on a digital quantum processor", Physical Review Research 7 3, 033153 (2025).

[206] Qi Zhao and Xiao Yuan, "Exploiting anticommutation in Hamiltonian simulation", Quantum 5, 534 (2021).

[207] Jeongbin Jo, "Deterministic ground state preparation via power-cosine filtering of time evolution operators", Physics Letters A 590, 131813 (2026).

[208] Omer Rathore, Alastair Basden, Nicholas Chancellor, and Halim Kusumaatmaja, "Encoding strategies for quantum enhanced fluid simulations: opportunities and challenges", Quantum Science and Technology 11 4, 043003 (2026).

[209] Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan, "Quantum Algorithms for Quantum Chemistry and Quantum Materials Science", Chemical Reviews 120 22, 12685 (2020).

[210] Kaoru Mizuta, "Nearly optimal quasienergy estimation and eigenstate preparation of time-periodic Hamiltonians by Sambe space formalism", Physical Review Research 7 1, 013068 (2025).

[211] Weijie Du and James P. Vary, "Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers", Physics Letters B 866, 139548 (2025).

[212] S Flannigan, N Pearson, G H Low, A Buyskikh, I Bloch, P Zoller, M Troyer, and A J Daley, "Propagation of errors and quantitative quantum simulation with quantum advantage", Quantum Science and Technology 7 4, 045025 (2022).

[213] Jinchuan Yang, Shiping He, Mingqiang Bai, and Zhiwen Mo, "Quantum positive matrix-positive matrix multiplication algorithm", Journal of Physics A: Mathematical and Theoretical 57 43, 435305 (2024).

[214] Vijay Balasubramanian, Matthew DeCross, Arjun Kar, and Onkar Parrikar, "Quantum complexity of time evolution with chaotic Hamiltonians", Journal of High Energy Physics 2020 1, 134 (2020).

[215] Joao F. Doriguello, Debbie Lim, Chi Seng Pun, Patrick Rebentrost, and Tushar Vaidya, "Quantum Algorithms for the Pathwise Lasso", Quantum 9, 1674 (2025).

[216] Dario Rocca, Cristian L. Cortes, Jérôme F. Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization", Journal of Chemical Theory and Computation 20 11, 4639 (2024).

[217] Patrick Rall and Bryce Fuller, "Amplitude Estimation from Quantum Signal Processing", Quantum 7, 937 (2023).

[218] Luis A. Martínez-Martínez, Tzu-Ching Yen, and Artur F. Izmaylov, "Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation", Quantum 7, 1086 (2023).

[219] Kaitian Gao, Youlong Yang, and Zhenye Du, "Quantum algorithm for low-rank matrix regression with feature extraction", Journal of Applied Physics 139 1, 014402 (2026).

[220] Abhijeet Alase, Robert R. Nerem, Mohsen Bagherimehrab, Peter Høyer, and Barry C. Sanders, "Tight bound for estimating expectation values from a system of linear equations ", Physical Review Research 4 2, 023237 (2022).

[221] Tianfeng Feng, Jue Xu, Wenjun Yu, Zekun Ye, Penghui Yao, and Qi Zhao, "Distributed Quantum Simulation", Physical Review Letters 137 16, 160601 (2026).

[222] I. Joseph, Y. Shi, M. D. Porter, A. R. Castelli, V. I. Geyko, F. R. Graziani, S. B. Libby, and J. L. DuBois, "Quantum computing for fusion energy science applications", Physics of Plasmas 30 1, 010501 (2023).

[223] Mostafizur Rahaman Laskar, Subhadeep Mondal, and Amit Kumar Dutta, "Eigen-Spectrum Estimation and Source Detection in a Massive Sensor Array Based on Quantum Assisted Hamiltonian Simulation Framework", IEEE Transactions on Communications 70 6, 4013 (2022).

[224] Anirban N. Chowdhury, Rolando D. Somma, and Yiğit Subaşı, "Computing partition functions in the one-clean-qubit model", Physical Review A 103 3, 032422 (2021).

[225] Sander Gribling, Iordanis Kerenidis, and Dániel Szilágyi, "An Optimal Linear-combination-of-unitaries-based Quantum Linear System Solver", ACM Transactions on Quantum Computing 5 2, 1 (2024).

[226] Hai-Ling Liu, Chao-Hua Yu, Lin-Chun Wan, Su-Juan Qin, Fei Gao, and Qiaoyan Wen, "Quantum mean centering for block-encoding-based quantum algorithm", Physica A: Statistical Mechanics and its Applications 607, 128227 (2022).

[227] Katsuhiro Endo and Kazuaki Z. Takahashi, "Divergence-free algorithms for solving nonlinear differential equations on quantum computers", Physical Review Research 8 1, 013057 (2026).

[228] Dong An, Pedro C. S. Costa, and Dominic W. Berry, "Large time-step discretization of adiabatic quantum dynamics", Physical Review Research 8 4, 043098 (2026).

[229] Malte Schade, Cyrill Bösch, Václav Hapla, and Andreas Fichtner, "A quantum computing concept for 1-D elastic wave simulation with exponential speedup", Geophysical Journal International 238 1, 321 (2024).

[230] Xi Lu, Yuan Liu, and Hongwei Lin, "Quantum Signal Processing and Quantum Singular Value Transformation on U(N)", Quantum 10, 2048 (2026).

[231] Erenay Karacan, "Phase estimation with compressed controlled time evolution", Physical Review A 113 4, 042420 (2026).

[232] Shantanav Chakraborty, Aditya Morolia, and Anurudh Peduri, "Quantum Regularized Least Squares", Quantum 7, 988 (2023).

[233] Yu Tanaka, Hayata Yamasaki, and Mio Murao, "Quantum state preparation via free binary decision diagram", Journal of Physics A: Mathematical and Theoretical 59 26, 265302 (2026).

[234] Keren Li and Pan Gao, "A NISQ Method to Simulate Hermitian Matrix Evolution", Entropy 24 7, 899 (2022).

[235] Pablo A. M. Casares, Roberto Campos, and M. A. Martin-Delgado, "TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry", Quantum 6, 768 (2022).

[236] Suguru Endo, Jinzhao Sun, Ying Li, Simon C. Benjamin, and Xiao Yuan, "Variational Quantum Simulation of General Processes", Physical Review Letters 125 1, 010501 (2020).

[237] Adam R. Brown, "Polynomial Equivalence of Complexity Geometries", Quantum 8, 1391 (2024).

[238] Martina Nibbi and Christian B. Mendl, "Block encoding of matrix product operators", Physical Review A 110 4, 042427 (2024).

[239] Yuki Sato, Ruho Kondo, Ikko Hamamura, Tamiya Onodera, and Naoki Yamamoto, "Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits", Physical Review Research 6 3, 033246 (2024).

[240] Daniele Cuomo and Robert van Leeuwen, "Quantum simulation in imaginary time for gauge-invariant models", Physica Scripta 101 13, 135106 (2026).

[241] Youle Wang and Linyun Cao, "Quantum phase transition detection via quantum support vector machine", Quantum Science and Technology 10 1, 015043 (2025).

[242] Jordi Weggemans, "Lower Bounds for Unitary Property Testing with Proofs and Advice", Quantum 9, 1717 (2025).

[243] Youle Wang, Wenbin Yu, Yanfeng Fan, and Lei Zhang, "PIQS: an efficient quantum subspace method for dynamical property estimation", Quantum Science and Technology 11 2, 025013 (2026).

[244] Daan Camps, Efekan Kökcü, Lindsay Bassman Oftelie, Wibe A. de Jong, Alexander F. Kemper, and Roel Van Beeumen, "An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation", SIAM Journal on Matrix Analysis and Applications 43 3, 1084 (2022).

[245] Yanbing Zhang, Tingting Song, and Zhihao Wu, "An improved quantum algorithm for support matrix machines", Quantum Information Processing 20 7, 229 (2021).

[246] Maxine Luo and J. Ignacio Cirac, "Efficient Simulation of Quantum Chemistry Problems in an Enlarged Basis Set", PRX Quantum 6 1, 010355 (2025).

[247] J.-T. Bu, Lei Zhang, Zhan Yu, Jing-Bo Wang, W.-Q. Ding, W.-F. Yuan, B. Wang, H.-J. Du, W.-J. Chen, L. Chen, J.-W. Zhang, J.-C. Li, F. Zhou, Xin Wang, and M. Feng, "Exploring the experimental limit of deep quantum signal processing using a trapped-ion simulator", Physical Review Applied 23 3, 034073 (2025).

[248] Osama Muhammad Raisuddin and Suvranu De, "A Review of Quantum Scientific Computing Algorithms Relevant to Computational Mechanics", Archives of Computational Methods in Engineering 33 1, 745 (2026).

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[250] Daniel Marti-Dafcik, Hugh G. A. Burton, and David P. Tew, "Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers", Physical Review Research 7 1, 013191 (2025).

[251] Yuntao Gu, Louis Hector, Paolo Giusto, Matthew Titsworth, Alok Warey, Dnyanesh Rajpathak, Eser Atesoglu, Ivan A. Burenkov, Philip R. Hemmer, and Alan L. Migdall, Quantum Computing, Communication, and Simulation VI 53 (2026) ISBN:9781510697553.

[252] Sophia Simon, Raffaele Santagati, Matthias Degroote, Nikolaj Moll, Michael Streif, and Nathan Wiebe, "Improved Precision Scaling for Simulating Coupled Quantum-Classical Dynamics", PRX Quantum 5 1, 010343 (2024).

[253] Caesnan M.G. Leditto, Angus Southwell, Behnam Tonekaboni, Gregory A.L. White, Muhammad Usman, and Kavan Modi, "Topological signal processing on quantum computers for higher-order network analysis", Physical Review Applied 23 5, 054054 (2025).

[254] Shi Jin, Nana Liu, and Yue Yu, "Quantum circuits for the heat equation with physical boundary conditions via Schrödingerization", Journal of Computational Physics 538, 114138 (2025).

[255] Hirofumi Nishi, Taichi Kosugi, Yusuke Nishiya, and Yu-ichiro Matsushita, "Quadratic acceleration of multistep probabilistic algorithms for state preparation", Physical Review Research 6 2, L022041 (2024).

[256] Gian Gentinetta, Friederike Metz, and Giuseppe Carleo, "Correcting and Extending Trotterized Quantum Many-Body Dynamics", PRX Quantum 6 3, 030361 (2025).

[257] Alexander Zlokapa and Rolando D. Somma, "Hamiltonian simulation for low-energy states with optimal time dependence", Quantum 8, 1449 (2024).

[258] Andrew Jackson, Theodoros Kapourniotis, and Animesh Datta, "Partition-function estimation: Quantum and quantum-inspired algorithms", Physical Review A 107 1, 012421 (2023).

[259] Kaoru Mizuta and Keisuke Fujii, "Optimal Hamiltonian simulation for time-periodic systems", Quantum 7, 962 (2023).

[260] Alexander Engel, Graeme Smith, and Scott E. Parker, "Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms", Physics of Plasmas 28 6, 062305 (2021).

[261] Michael Norval and Zenghui Wang, "Quantum AI in Speech Emotion Recognition", Entropy 27 12, 1201 (2025).

[262] Michael P. Kaicher, Simon B. Jäger, Pierre-Luc Dallaire-Demers, and Frank K. Wilhelm, "Roadmap for quantum simulation of the fractional quantum Hall effect", Physical Review A 102 2, 022607 (2020).

[263] Nhat A. Nghiem and Tzu-Chieh Wei, "Quantum algorithm for estimating largest eigenvalues", Physics Letters A 488, 129138 (2023).

[264] Davide Veronelli, Francesca Cibrario, Emanuele Dri, Valeria Zaffaroni, Giacomo Ranieri, Davide Corbelletto, and Bartolomeo Montrucchio, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2228 (2025) ISBN:979-8-3315-5736-2.

[265] John M. Martyn, Zane M. Rossi, Kevin Z. Cheng, Yuan Liu, and Isaac L. Chuang, "Parallel Quantum Signal Processing Via Polynomial Factorization", Quantum 9, 1834 (2025).

[266] Tejas Shinde, Ljubomir Budinski, Ossi Niemimäki, Valtteri Lahtinen, Helena Liebelt, and Rui Li, "Utilizing classical programming principles in the Intel Quantum SDK: implementation of quantum lattice Boltzmann method", ACM Transactions on Quantum Computing 6 1, 1 (2025).

[267] Marcela Carena, Erik J. Gustafson, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Gauge theory couplings on anisotropic lattices", Physical Review D 106 11, 114504 (2022).

[268] Shota Kanasugi, Yuichiro Hidaka, Yuya O. Nakagawa, Shoichiro Tsutsui, Norifumi Matsumoto, Kazunori Maruyama, Hirotaka Oshima, and Shintaro Sato, "Subspace-based local compilation of variational quantum circuits for large-scale quantum many-body simulation", Physical Review Research 7 2, 023298 (2025).

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[270] Tatsuki Odake, Hlér Kristjánsson, Philip Taranto, and Mio Murao, "Universal algorithm for transforming Hamiltonian eigenvalues", Physical Review Research 7 1, 013331 (2025).

[271] Yihui Quek and Patrick Rebentrost, "Fast algorithm for quantum polar decomposition and applications", Physical Review Research 4 1, 013144 (2022).

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[273] Roman Novak, "Quantum Algorithms in Electromagnetic Propagation Modelling for Telecommunications", IEEE Access 11, 111545 (2023).

[274] Xi-Ning Zhuang, Zhao-Yun Chen, Yu-Chun Wu, and Guo-Ping Guo, "Quantum computational quantitative trading: high-frequency statistical arbitrage algorithm", New Journal of Physics 24 7, 073036 (2022).

[275] Paul K. Faehrmann, Jens Eisert, and Richard Kueng, "In the Shadow of the Hadamard Test: Using the Garbage State for Good and Further Modifications", Physical Review Letters 135 15, 150603 (2025).

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[277] Yuan Su, "Framework for Hamiltonian simulation and beyond: standard-form encoding, qubitization, and quantum signal processing", Quantum Views 3, 21 (2019).

[278] Andrew M. Childs and Yuan Su, "Nearly Optimal Lattice Simulation by Product Formulas", Physical Review Letters 123 5, 050503 (2019).

[279] Yatian Wang, Hua Xiang, and Songling Zhang, "Quantum algorithm for matrix logarithm by integral formula", Quantum Information Processing 22 1, 76 (2023).

[280] Manuel G. Algaba, P. V. Sriluckshmy, Martin Leib, and Fedor Šimkovic IV, "Low-depth simulations of fermionic systems on square-grid quantum hardware", Quantum 8, 1327 (2024).

[281] Ahmet Burak Catli, Sophia Simon, and Nathan Wiebe, "Efficient Quantum Optimization via Dynamical Simulation", PRX Quantum 7 3, 033026 (2026).

[282] Daniel Bultrini and Oriol Vendrell, "Mixed quantum-classical dynamics for near term quantum computers", Communications Physics 6 1, 328 (2023).

[283] Ryan Shaffer, Hang Ren, Emiliia Dyrenkova, Christopher G. Yale, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, and Hartmut Häffner, "Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors", Quantum 7, 997 (2023).

[284] Yue Wang and Qi Zhao, "Randomization accelerating series-truncated quantum algorithms", Physical Review A 113 4, 042423 (2026).

[285] Sevag Gharibian and François Le Gall, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing 19 (2022) ISBN:9781450392648.

[286] Ruizhe Zhang, Guoming Wang, and Peter Johnson, "Computing Ground State Properties with Early Fault-Tolerant Quantum Computers", Quantum 6, 761 (2022).

[287] Kazuki Sakamoto, Hayata Morisaki, Junichi Haruna, Etsuko Itou, Keisuke Fujii, and Kosuke Mitarai, "End-to-end complexity for simulating the Schwinger model on quantum computers", Quantum 8, 1474 (2024).

[288] A. Roggero, "Spectral-density estimation with the Gaussian integral transform", Physical Review A 102 2, 022409 (2020).

[289] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson, "The Variational Quantum Eigensolver: A review of methods and best practices", Physics Reports 986, 1 (2022).

[290] Gumaro Rendon, Jacob Watkins, and Nathan Wiebe, "Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation", Quantum 8, 1266 (2024).

[291] Chetra Mang, Sunheang Ty, Axel TahmasebiMoradi, Renaud Vilmart, and Rim Kaddah, Communications in Computer and Information Science 2744, 167 (2026) ISBN:978-3-032-13854-5.

[292] "Circuit compilation and error mitigation for near-term quantum computing", Université de Montpellier (2022-....) (2022).

[293] Sina Zeytinoğlu and Sho Sugiura, "Error-robust quantum signal processing using Rydberg atoms", Physical Review Research 6 1, 013003 (2024).

[294] Joe Gibbs, Kaitlin Gili, Zoë Holmes, Benjamin Commeau, Andrew Arrasmith, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, "Long-time simulations for fixed input states on quantum hardware", npj Quantum Information 8 1, 135 (2022).

[295] Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf, "Quantum SDP-Solvers: Better upper and lower bounds", Quantum 4, 230 (2020).

[296] Siddharth Hariprakash, Neel S. Modi, Michael Kreshchuk, Christopher F. Kane, and Christian W. Bauer, "Strategies for simulating the time evolution of Hamiltonian lattice field theories", Physical Review A 111 2, 022419 (2025).

[297] Dong An, Di Fang, and Lin Lin, "Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation", Quantum 6, 690 (2022).

[298] Kenji Sugisaki, "Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?", AIP Advances 14 9, 095021 (2024).

[299] Timo Eckstein, Refik Mansuroglu, Piotr Czarnik, Jian-Xin Zhu, Michael J. Hartmann, Lukasz Cincio, Andrew T. Sornborger, and Zoë Holmes, "Large-scale simulations of Floquet physics on near-term quantum computers", npj Quantum Information 10 1, 84 (2024).

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[301] Thomas E. O’Brien, Lev B. Ioffe, Yuan Su, David Fushman, Hartmut Neven, Ryan Babbush, and Vadim Smelyanskiy, "Quantum Computation of Molecular Structure Using Data from Challenging-To-Classically-Simulate Nuclear Magnetic Resonance Experiments", PRX Quantum 3 3, 030345 (2022).

[302] Robin OLLIVE and Stephane LOUISE, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 256 (2024) ISBN:979-8-3315-4137-8.

[303] Dominik Hangleiter and Jens Eisert, "Computational advantage of quantum random sampling", Reviews of Modern Physics 95 3, 035001 (2023).

[304] Matthew Hagan and Nathan Wiebe, "Composite Quantum Simulations", Quantum 7, 1181 (2023).

[305] Zane M. Rossi and Isaac L. Chuang, "Quantum hypothesis testing with group structure", Physical Review A 104 1, 012425 (2021).

[306] Tae-Won Kim and Byung-Soo Choi, "Analysis of quantum primitives for quantum utility", Quantum Information Processing 25 6, 181 (2026).

[307] Chen He, Jiazhen Li, Weiqi Liu, Jinye Peng, and Z. Jane Wang, "A Low-Complexity Quantum Principal Component Analysis Algorithm", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[308] Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, and Thomas Rung, "Quantum algorithm for the advection-diffusion equation by direct block encoding of the time-marching operator", Physical Review A 112 1, L010401 (2025).

[309] Tyler Kharazi, Torin F. Stetina, Liwen Ko, Guang Hao Low, and K. Birgitta Whaley, "An efficient quantum algorithm for ab initio approximations of non-linear response functions", npj Quantum Information 11 1, 98 (2025).

[310] Shi Jin, Xiantao Li, Nana Liu, and Yue Yu, "Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions", SIAM Journal on Scientific Computing 46 4, B403 (2024).

[311] Ryotaro Niwa, Zane Marius Rossi, Philip Taranto, and Mio Murao, "Singular value transformation for unknown quantum channels", Physical Review A 114 3, L030401 (2026).

[312] Yue Yu, Yulin Chi, Chonghao Zhai, Jieshan Huang, Qihuang Gong, and Jianwei Wang, "Programmable silicon-photonic quantum simulator based on a linear combination of unitaries", Photonics Research 12 8, 1760 (2024).

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[314] Weiyuan Gong, Si Jiang, and Dong-Ling Deng, "No-go theorem and a universal decomposition strategy for quantum channel compilation", Physical Review Research 5 1, 013060 (2023).

[315] Scott E. Smart and David A. Mazziotti, "Many-fermion simulation from the contracted quantum eigensolver without fermionic encoding of the wave function", Physical Review A 105 6, 062424 (2022).

[316] Mario Motta, Tanvi P. Gujarati, Julia E. Rice, Ashutosh Kumar, Conner Masteran, Joseph A. Latone, Eunseok Lee, Edward F. Valeev, and Tyler Y. Takeshita, "Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer", Physical Chemistry Chemical Physics 22 42, 24270 (2020).

[317] Mario Motta, William Kirby, Ieva Liepuoniute, Kevin J Sung, Jeffrey Cohn, Antonio Mezzacapo, Katherine Klymko, Nam Nguyen, Nobuyuki Yoshioka, and Julia E Rice, "Subspace methods for electronic structure simulations on quantum computers", Electronic Structure 6 1, 013001 (2024).

[318] Chunlin Yang, Zexian Li, Hongmei Yao, Zhaobing Fan, Guofeng Zhang, and Jianshe Liu, "Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth", Quantum 9, 1805 (2025).

[319] Rawad Mezher, Ana Filipa Carvalho, and Shane Mansfield, "Solving graph problems with single photons and linear optics", Physical Review A 108 3, 032405 (2023).

[320] Javier Gonzalez-Conde, Zachary Morrell, Marc Vuffray, Tameem Albash, and Carleton Coffrin, "Cost of emulating a small quantum annealing problem in the circuit model", Physical Review A 111 6, 062606 (2025).

[321] Duarte Magano and Miguel Murça, "Simplifying a classical-quantum algorithm interpolation with quantum singular value transformations", Physical Review A 106 6, 062419 (2022).

[322] Shi Jin, Nana Liu, and Chuwen Ma, "Quantum simulation of Maxwell’s equations via Schrödingerisation", ESAIM: Mathematical Modelling and Numerical Analysis 58 5, 1853 (2024).

[323] Ze-Tong Li, Fan-Xu Meng, Xu-Tao Yu, and Zai-Chen Zhang, "Quantum algorithm for Laplacian eigenmap via Rayleigh quotient iteration", Quantum Information Processing 21 1, 11 (2022).

[324] Melody Lee, Zhixin Song, Sriharsha Kocherla, Austin Adams, Alexander Alexeev, and Spencer H. Bryngelson, "A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method", Future Generation Computer Systems 174, 107975 (2026).

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[326] William Kirby, "Analysis of quantum Krylov algorithms with errors", Quantum 8, 1457 (2024).

[327] Nhat A. Nghiem and Tzu-Chieh Wei, "Estimation of nonlinear physical quantities by measuring ancillas", Physical Review A 112 6, 062412 (2025).

[328] Tong Ning, Youlong Yang, and Zhenye Du, "Quantum algorithm for twin extreme learning machine", Physica Scripta 98 8, 085110 (2023).

[329] Zhiyan Ding, Marius Junge, Philipp Schleich, and Peixue Wu, "Lower Bound for Simulation Cost of Open Quantum Systems: Lipschitz Continuity Approach", Communications in Mathematical Physics 406 3, 60 (2025).

[330] Shantanav Chakraborty, Leonardo Novo, and Jérémie Roland, "Finding a marked node on any graph via continuous-time quantum walks", Physical Review A 102 2, 022227 (2020).

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[599] Jumpei Kato, Kaito Wada, Kosuke Ito, and Naoki Yamamoto, "Exponentially Accurate Open Quantum Simulation via Randomized Dissipation with Minimal Ancilla", PRX Quantum 7 3, 033046 (2026).

[600] Alain Delgado, Pablo A. M. Casares, Roberto dos Reis, Modjtaba Shokrian Zini, Roberto Campos, Norge Cruz-Hernández, Arne-Christian Voigt, Angus Lowe, Soran Jahangiri, M. A. Martin-Delgado, Jonathan E. Mueller, and Juan Miguel Arrazola, "Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer", Physical Review A 106 3, 032428 (2022).

[601] Yudai Suzuki, Bi Hong Tiang, Jeongrak Son, Nelly H. Y. Ng, Zoe Holmes, and Marek Gluza, "Double-bracket algorithm for quantum signal processing without post-selection", Quantum 9, 1954 (2025).

[602] Roman Novak, "Quantum Algorithm for Solving the Wave Equation on a Hexagonal Grid", IEEE Access 12, 131009 (2024).

[603] Roberto Campos, P. A. M. Casares, and M. A. Martin-Delgado, "Quantum Metropolis Solver: a quantum walks approach to optimization problems", Quantum Machine Intelligence 5 2, 28 (2023).

[604] John M. Martyn, Yuan Liu, Zachary E. Chin, and Isaac L. Chuang, "Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation", The Journal of Chemical Physics 158 2, 024106 (2023).

[605] Lin-Chun Wan, Chao-Hua Yu, Shi-Jie Pan, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen, "Block-encoding-based quantum algorithm for linear systems with displacement structures", Physical Review A 104 6, 062414 (2021).

[606] Jessica Lemieux, Bettina Heim, David Poulin, Krysta Svore, and Matthias Troyer, "Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm", Quantum 4, 287 (2020).

[607] Matthew Otten, Matthew R. Hermes, Riddhish Pandharkar, Yuri Alexeev, Stephen K. Gray, and Laura Gagliardi, "Localized Quantum Chemistry on Quantum Computers", Journal of Chemical Theory and Computation 18 12, 7205 (2022).

[608] Matthew X Burns, Chenxu Liu, Samuel Stein, Bo Peng, Karol Kowalski, and Ang Li, "GALIC: hybrid multi-qubitwise pauli grouping for quantum computing measurement", Quantum Science and Technology 10 1, 015054 (2025).

[609] Ashish Joshi and Takahiko Koyama, "Quantum Algorithm for Metabolic Network Analysis", (2025).

[610] William Kirby, Mario Motta, and Antonio Mezzacapo, "Exact and efficient Lanczos method on a quantum computer", Quantum 7, 1018 (2023).

[611] Guangsheng Ma and Ziwei Zhou, "Great-length wavelets on quantum computing platform: Applications and fast approximations", Signal Processing 220, 109472 (2024).

[612] Sihao Wu, Weijie Du, Xingbo Zhao, and James P. Vary, "Efficient and precise quantum simulation of ultrarelativistic quark-nucleus scattering", Physical Review D 110 5, 056044 (2024).

[613] Zi-Jian Zhang, Jinzhao Sun, Xiao Yuan, and Man-Hong Yung, "Low-Depth Hamiltonian Simulation by an Adaptive Product Formula", Physical Review Letters 130 4, 040601 (2023).

[614] Michał Szczepanik, Ákos Nagy, and Emil Zak, "Simulating high-accuracy nuclear motion Hamiltonians using discrete variable representation and Walsh–Hadamard QROM on fault-tolerant quantum computers", Quantum Science and Technology 11 4, 045039 (2026).

[615] Zi-Ming Li and Yu-xi Liu, "Quantum algorithm for vector set orthogonal normalization and matrix QR decomposition with polynomial speedup", Physical Review A 112 3, 032410 (2025).

[616] S.N. Saadatmand, Tyler L. Wilson, Mark J. Hodson, Mark Field, Simon J. Devitt, Madhav Krishnan Vijayan, Alan Robertson, Thinh P. Le, Jannis Ruh, Alexandru Paler, Arshpreet Singh Maan, Ioana Moflic, Athena Caesura, and Josh Y. Mutus, "Superconducting qubits in the millions: The potential and limitations of modularity", Physical Review Applied 25 6, 064038 (2026).

[617] Pei Yuan and Shengyu Zhang, "Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits", Quantum 7, 956 (2023).

[618] Saeid Abbasbandy, "Treatment of linear and nonlinear pantograph equations with a quantum pseudo-spectral method", Physica Scripta 101 25, 255204 (2026).

[619] Di Fang, Lin Lin, and Yu Tong, "Time-marching based quantum solvers for time-dependent linear differential equations", Quantum 7, 955 (2023).

[620] Guang Hao Low, Vadym Kliuchnikov, and Luke Schaeffer, "Trading T gates for dirty qubits in state preparation and unitary synthesis", Quantum 8, 1375 (2024).

[621] Mauro E. S. Morales, Lirandë Pira, Philipp Schleich, Kelvin Koor, Pedro C. S. Costa, Dong An, Alán Aspuru-Guzik, Lin Lin, Patrick Rebentrost, and Dominic W. Berry, "Quantum linear system solvers: A survey of algorithms and applications", Reviews of Modern Physics 98 2, 025005 (2026).

[622] Kaoru Mizuta, Yuya O. Nakagawa, Kosuke Mitarai, and Keisuke Fujii, "Local Variational Quantum Compilation of Large-Scale Hamiltonian Dynamics", PRX Quantum 3 4, 040302 (2022).

[623] Jingwei Wen, Guoqing Qin, Chao Zheng, Shijie Wei, Xiangyu Kong, Tao Xin, and Guilu Long, "Observation of information flow in the anti-𝒫𝒯-symmetric system with nuclear spins", npj Quantum Information 6 1, 28 (2020).

[624] Nhat A. Nghiem, Hiroki Sukeno, Shuyu Zhang, and Tzu-Chieh Wei, "Improved quantum power method and numerical integration using a quantum singular-value transformation", Physical Review A 111 1, 012434 (2025).

[625] Yan Wang, Sarah Chehade, and Eugene Dumitrescu, "Semicoherent symmetric quantum processes: Theory and applications", AVS Quantum Science 6 3, 033805 (2024).

[626] Yusen Wu and Jingbo B Wang, "Estimating Gibbs partition function with quantum Clifford sampling", Quantum Science and Technology 7 2, 025006 (2022).

[627] Mario Motta and Julia E. Rice, "Emerging quantum computing algorithms for quantum chemistry", WIREs Computational Molecular Science 12 3, e1580 (2022).

[628] Yu Tong, Victor V. Albert, Jarrod R. McClean, John Preskill, and Yuan Su, "Provably accurate simulation of gauge theories and bosonic systems", Quantum 6, 816 (2022).

[629] Lane G. Gunderman, Andrew Jena, and Luca Dellantonio, "Minimal qubit representations of Hamiltonians via conserved charges", Physical Review A 109 2, 022618 (2024).

[630] Han Qi, Liyuan Wang, Changqing Gong, and Abdullah Gani, "A survey on quantum data mining algorithms: challenges, advances and future directions", Quantum Information Processing 23 3, 74 (2024).

[631] Einar Gabbassov, "Stochastic Schrödinger equations for quantum reverse diffusion", Physical Review Research 8 2, 023329 (2026).

[632] Michael Kreshchuk, Shaoyang Jia, William M. Kirby, Gary Goldstein, James P. Vary, and Peter J. Love, "Simulating hadronic physics on noisy intermediate-scale quantum devices using basis light-front quantization", Physical Review A 103 6, 062601 (2021).

[633] Dyon van Vreumingen and Kareljan Schoutens, "Adiabatic ground-state preparation of fermionic many-body systems from a two-body perspective", Physical Review A 108 6, 062603 (2023).

[634] Marco Majland, Rasmus Berg Jensen, Patrick Ettenhuber, Irfansha Shaik, Nikolaj Thomas Zinner, and Ove Christiansen, "Fault-Tolerant Quantum Computations of Vibrational Wave Functions", Journal of Chemical Theory and Computation 22 1, 30 (2026).

[635] Yue Wang, Wenjun Yu, Tianfeng Feng, and Qi Zhao, "Advances in time-independent Hamiltonian simulation algorithms", Frontiers of Computer Science 20 10, 2010909 (2026).

[636] Tillman Philo and Caglar Oskay, "PHASE: Pauli Hierarchical Assembly on Subdivided Elements for quantum-compatible operator synthesis", Computer Methods in Applied Mechanics and Engineering 463, 119424 (2027).

[637] I. Novikau and I. Joseph, "An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations", Journal of Computational Physics 564, 115132 (2026).

[638] Matteo Scandi and Álvaro M. Alhambra, "Thermalization in Open Many-Body Systems and KMS Detailed Balance", Physical Review X 16 1, 011040 (2026).

[639] Tom O'Leary, Lewis W. Anderson, Dieter Jaksch, and Martin Kiffner, "Partitioned Quantum Subspace Expansion", Quantum 9, 1726 (2025).

[640] Sumeet, Srinivasa Prasannaa V, Bhanu Pratap Das, and Bijaya Kumar Sahoo, "Assessing the Precision of Quantum Simulation of Many-Body Effects in Atomic Systems Using the Variational Quantum Eigensolver Algorithm", Quantum Reports 4 2, 173 (2022).

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[642] Julien Zylberman and Fabrice Debbasch, "Efficient quantum state preparation with Walsh series", Physical Review A 109 4, 042401 (2024).

[643] Eneet Kaur, Shahrooz Pouryousef, Hassan Shapourian, Jiapeng Zhao, Michael Kilzer, Ramana Kompella, and Reza Nejabati, "Optimized Quantum Circuit Partitioning Across Multiple Quantum Processors", IEEE Transactions on Quantum Engineering 6, 1 (2025).

[644] Patrick Rall, "Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation", Quantum 5, 566 (2021).

[645] Brayden Goldstein-Gelb, Kun Liu, John M. Martyn, Hengyun (Harry) Zhou, Yongshan Ding, and Yuan Liu, Proceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 426 (2026) ISBN:9798400723599.

[646] Davide Orsucci and Vedran Dunjko, "On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number", Quantum 5, 573 (2021).

[647] Ryan Babbush, William J. Huggins, Dominic W. Berry, Shu Fay Ung, Andrew Zhao, David R. Reichman, Hartmut Neven, Andrew D. Baczewski, and Joonho Lee, "Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods", Nature Communications 14 1, 4058 (2023).

[648] Yuichiro Hidaka, Shoichiro Tsutsui, Shota Kanasugi, Norifumi Matsumoto, Kazunori Maruyama, and Hirotaka Oshima, "Fast-forwardability of qubit-mapped fermion models based on Cartan decomposition", Physical Review Research 8 3, 033251 (2026).

[649] Sina Zeytinoğlu, "Generalized parity measurements and efficient large multicomponent cat state preparation with quantum signal processing", Physical Review Research 8 2, 023208 (2026).

[650] Robbie King, Guang Hao Low, Ryan Babbush, Rolando D. Somma, and Nicholas C. Rubin, "Quantum Simulation with Sum-of-Squares Spectral Amplification", Physical Review Letters 136 11, 110601 (2026).

[651] Oriel Kiss, Utkarsh Azad, Borja Requena, Alessandro Roggero, David Wakeham, and Juan Miguel Arrazola, "Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation", Quantum 9, 1682 (2025).

[652] Zhiyan Ding, Bowen Li, and Lin Lin, "Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition", Communications in Mathematical Physics 406 3, 67 (2025).

[653] Avimita Chatterjee, Sonny Rappaport, Anish Giri, Sonika Johri, Timothy Proctor, David E. Bernal Neira, Pratik Sathe, and Thomas Lubinski, "A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations", IEEE Transactions on Quantum Engineering 6, 1 (2025).

[654] Ryan Babbush, Dominic W. Berry, Robin Kothari, Rolando D. Somma, and Nathan Wiebe, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) 405 (2023) ISBN:979-8-3503-1894-4.

[655] Yuan Su, Dominic W. Berry, Nathan Wiebe, Nicholas Rubin, and Ryan Babbush, "Fault-Tolerant Quantum Simulations of Chemistry in First Quantization", PRX Quantum 2 4, 040332 (2021).

[656] Xiantao Li, "From Linear Differential Equations to Unitaries: A Moment-Matching Dilation Framework with Near-Optimal Quantum Algorithms", PRX Quantum 7 2, 020350 (2026).

[657] Abtin Ameri, Erika Ye, Paola Cappellaro, Hari Krovi, and Nuno F. Loureiro, "Quantum algorithm for the linear Vlasov equation with collisions", Physical Review A 107 6, 062412 (2023).

[658] Nicholas C. Rubin, Dominic W. Berry, Alina Kononov, Fionn D. Malone, Tanuj Khattar, Alec White, Joonho Lee, Hartmut Neven, Ryan Babbush, and Andrew D. Baczewski, "Quantum computation of stopping power for inertial fusion target design", Proceedings of the National Academy of Sciences 121 23, e2317772121 (2024).

[659] Burak Şahinoğlu and Rolando D. Somma, "Hamiltonian simulation in the low-energy subspace", npj Quantum Information 7 1, 119 (2021).

[660] Phillip W. K. Jensen, Peter D. Johnson, and Alexander A. Kunitsa, "Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods", Physical Review A 108 2, 022422 (2023).

[661] Suraj Goel, Matthew Reynolds, Matthew Girling, Will McCutcheon, Saroch Leedumrongwatthanakun, Vatshal Srivastav, David Jennings, Mehul Malik, and Jiannis K. Pachos, "Unveiling the Non-Abelian Statistics of D(S3) Anyons Using a Classical Photonic Simulator", Physical Review Letters 132 11, 110601 (2024).

[662] Jeongrak Son, Marek Gluza, Ryuji Takagi, and Nelly H. Y. Ng, "Quantum Dynamic Programming", Physical Review Letters 134 18, 180602 (2025).

[663] Shi Jin and Nana Liu, "Quantum algorithms for nonlinear partial differential equations", Bulletin des Sciences Mathématiques 194, 103457 (2024).

[664] Younes Javanmard, Ugne Liaubaite, Tobias J. Osborne, Xusheng Xu, and Man-Hong Yung, "Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries", APL Quantum 1 4, 046114 (2024).

[665] Ignacio Loaiza, Aritra Sankar Brahmachari, and Artur F Izmaylov, "Majorana tensor decomposition: a unifying framework for decompositions of fermionic Hamiltonians to linear combination of unitaries", Quantum Science and Technology 10 3, 035035 (2025).

[666] Alireza Ataei, Olle Eriksson, and Vahid Azimi-Mousolou, "Ground-state preparation via nonlinear quantum dissipation", Physical Review B 114 20, 204407 (2026).

[667] Teague Tomesh, Pranav Gokhale, Victory Omole, Gokul Subramanian Ravi, Kaitlin N. Smith, Joshua Viszlai, Xin-Chuan Wu, Nikos Hardavellas, Margaret R. Martonosi, and Frederic T. Chong, 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 587 (2022) ISBN:978-1-6654-2027-3.

[668] Ryan Babbush, Dominic W. Berry, Jarrod R. McClean, and Hartmut Neven, "Quantum simulation of chemistry with sublinear scaling in basis size", npj Quantum Information 5 1, 92 (2019).

[669] Tony Metger and Henry Yuen, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) 1349 (2023) ISBN:979-8-3503-1894-4.

[670] Anthony Ciavarella, Natalie Klco, and Martin J. Savage, "Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis", Physical Review D 103 9, 094501 (2021).

[671] Daan Camps and Roel Van Beeumen, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 104 (2022) ISBN:978-1-6654-9113-6.

[672] Farshad Amani, Reza Mahroo, and Amin Kargarian, 2023 IEEE Texas Power and Energy Conference (TPEC) 1 (2023) ISBN:978-1-6654-9071-9.

[673] B. David Clader, Alexander M. Dalzell, Nikitas Stamatopoulos, Grant Salton, Mario Berta, and William J. Zeng, "Quantum Resources Required to Block-Encode a Matrix of Classical Data", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[674] Hirofumi Nishi, Yuki Takei, Taichi Kosugi, Shunsuke Mieda, Yutaka Natsume, Takeshi Aoyagi, and Yu-ichiro Matsushita, "Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits", Physical Review Applied 23 3, 034016 (2025).

[675] Smik Patel, Praveen Jayakumar, Rick Huang, Tao Zeng, and Artur F. Izmaylov, "Quantum Seniority-Based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem", Journal of Chemical Theory and Computation 22 8, 3937 (2026).

[676] Hefeng Wang, Sixia Yu, and Hua Xiang, "Efficient quantum algorithm for solving structured problems via multistep quantum computation", Physical Review Research 5 1, L012004 (2023).

[677] Ignacio Loaiza and Artur F. Izmaylov, "Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries", Journal of Chemical Theory and Computation 19 22, 8201 (2023).

[678] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan, "Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation", Journal of the Physical Society of Japan 90 3, 032001 (2021).

[679] Debjyoti Biswas, Gaurav M. Vaidya, and Prabha Mandayam, "Noise-adapted recovery circuits for quantum error correction", Physical Review Research 6 4, 043034 (2024).

[680] Sergi Abadal, Chong Han, Vitaly Petrov, Laura Galluccio, Ian F. Akyildiz, and Josep M. Jornet, "Electromagnetic Nanonetworks Beyond 6G: From Wearable and Implantable Networks to On-Chip and Quantum Communication", IEEE Journal on Selected Areas in Communications 42 8, 2122 (2024).

[681] Xin Wang, Mingrui Jing, and Chengkai Zhu, "Computable and Faithful Lower Bound on Entanglement Cost", Physical Review Letters 134 19, 190202 (2025).

[682] Joshua J. Goings, Alec White, Joonho Lee, Christofer S. Tautermann, Matthias Degroote, Craig Gidney, Toru Shiozaki, Ryan Babbush, and Nicholas C. Rubin, "Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers", Proceedings of the National Academy of Sciences 119 38, e2203533119 (2022).

[683] Yun-Zhuo Fan, Yu-Xia Wu, and Dan-Bo Zhang, "Adaptive random compiler for Hamiltonian simulation", Physical Review A 112 6, 062431 (2025).

[684] Michele Minervini, Dhrumil Patel, and Mark M. Wilde, "Evolved quantum Boltzmann machines", Physical Review A 113 3, 032427 (2026).

[685] George T. Fleming, Prasanth Shyamsundar, and Judah Unmuth-Yockey, "Fermion determinants on a quantum computer", Physical Review D 111 5, 054509 (2025).

[686] Matthias Rosenkranz, Eric Brunner, Gabriel Marin-Sanchez, Nathan Fitzpatrick, Silas Dilkes, Yao Tang, Yuta Kikuchi, and Marcello Benedetti, "Quantum state preparation for multivariate functions", Quantum 9, 1703 (2025).

[687] Hongbin Liu, Guang Hao Low, Damian S. Steiger, Thomas Häner, Markus Reiher, and Matthias Troyer, "Prospects of quantum computing for molecular sciences", Materials Theory 6 1, 11 (2022).

[688] Erik Lötstedt, Takanori Nishi, and Kaoru Yamanouchi, "Simulation of time-dependent quantum dynamics using quantum computers", Advances in Atomic Molecular and Optical Physics Advances In Atomic, Molecular, and Optical Physics 73, 33 (2024) ISBN:9780443314582.

[689] Savo Glisic and Beatriz Lorenzo, "Quantum computing and neuroscience for 6G/7G networks: Survey", Intelligent Systems with Applications 23, 200346 (2024).

[690] Abhishek Rajput, Alessandro Roggero, and Nathan Wiebe, "Hybridized Methods for Quantum Simulation in the Interaction Picture", Quantum 6, 780 (2022).

[691] David B. Kaplan and Jesse R. Stryker, "Gauss’s law, duality, and the Hamiltonian formulation of U(1) lattice gauge theory", Physical Review D 102 9, 094515 (2020).

[692] Thomas Ayral, "Classical and quantum algorithms for many-body problems", Comptes Rendus. Physique 26 G1, 25 (2025).

[693] Philipp Pfeffer, Peter Brearley, Sylvain Laizet, and Jörg Schumacher, "Spectral quantum algorithm for passive scalar transport in shear flows", Scientific Reports 15 1, 41172 (2025).

[694] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, "Faster Digital Quantum Simulation by Symmetry Protection", PRX Quantum 2 1, 010323 (2021).

[695] Xiao-Ming Zhang, "Robust and Optimal Loading of General Classical Data Into Quantum Computers", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 45 3, 1170 (2026).

[696] Simon Thelen and Wolfgang Mauerer, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 591 (2025) ISBN:979-8-3315-5736-2.

[697] Nhung H. Nguyen, Minh C. Tran, Yingyue Zhu, Alaina M. Green, C. Huerta Alderete, Zohreh Davoudi, and Norbert M. Linke, "Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions", PRX Quantum 3 2, 020324 (2022).

[698] Shuchen Zhu, Aarthi Sundaram, and Guang Hao Low, "Unified architecture for quantum lookup tables", Physical Review Research 7 4, 043230 (2025).

[699] Chan Gu Kang and Hakjoo Oh, "Modular Component-Based Quantum Circuit Synthesis", Proceedings of the ACM on Programming Languages 7 OOPSLA1, 348 (2023).

[700] Kushagra Garg, Zeeshan Ahmed, Subhadip Mitra, and Shantanav Chakraborty, "Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers", Physical Review A 112 2, 022425 (2025).

[701] Junan Lin and Artur F. Izmaylov, "Bounding eigenstate overlap from Hamiltonian moments: Success-probability guarantees for quantum phase estimation", Physical Review A 114 4, 042432 (2026).

[702] Ryo Watanabe, Keisuke Fujii, and Hiroshi Ueda, "Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz", Physical Review Research 6 2, 023009 (2024).

[703] Kaiwen Gui, Alexander M. Dalzell, Alessandro Achille, Martin Suchara, and Frederic T. Chong, "Spacetime-Efficient Low-Depth Quantum State Preparation with Applications", Quantum 8, 1257 (2024).

[704] Fanxu Meng, Zhiguo Huang, Yuan Long, Tian Luan, Xianchao Zhang, Xutao Yu, and Zaichen Zhang, "Multiagent reinforcement learning for efficient variational fast-forwarding quantum circuits", Physical Review A 113 1, 012618 (2026).

[705] Paul Beame, Niels Kornerup, and Michael Whitmeyer, "Quantum Time-Space Tradeoffs for Matrix Problems", SIAM Journal on Computing 55 3, 469 (2026).

[706] Sitan Chen, Jordan Cotler, Hsin-Yuan Huang, and Jerry Li, "The complexity of NISQ", Nature Communications 14 1, 6001 (2023).

[707] Le Hu and Andrew N. Jordan, "Quantum state driving along arbitrary trajectories", Physical Review Research 5 3, 033045 (2023).

[708] Alicia B. Magann, Matthew D. Grace, Herschel A. Rabitz, and Mohan Sarovar, "Digital quantum simulation of molecular dynamics and control", Physical Review Research 3 2, 023165 (2021).

[709] Joonho Lee, Dominic W. Berry, Craig Gidney, William J. Huggins, Jarrod R. McClean, Nathan Wiebe, and Ryan Babbush, "Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction", PRX Quantum 2 3, 030305 (2021).

[710] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, "Theory of Trotter Error with Commutator Scaling", Physical Review X 11 1, 011020 (2021).

[711] Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W. Bauer, Kerstin Borras, Stefano Carrazza, Arianna Crippa, Vincent Croft, Roland de Putter, Andrea Delgado, Vedran Dunjko, Daniel J. Egger, Elias Fernández-Combarro, Elina Fuchs, Lena Funcke, Daniel González-Cuadra, Michele Grossi, Jad C. Halimeh, Zoë Holmes, Stefan Kühn, Denis Lacroix, Randy Lewis, Donatella Lucchesi, Miriam Lucio Martinez, Federico Meloni, Antonio Mezzacapo, Simone Montangero, Lento Nagano, Vincent R. Pascuzzi, Voica Radescu, Enrique Rico Ortega, Alessandro Roggero, Julian Schuhmacher, Joao Seixas, Pietro Silvi, Panagiotis Spentzouris, Francesco Tacchino, Kristan Temme, Koji Terashi, Jordi Tura, Cenk Tüysüz, Sofia Vallecorsa, Uwe-Jens Wiese, Shinjae Yoo, and Jinglei Zhang, "Quantum Computing for High-Energy Physics: State of the Art and Challenges", PRX Quantum 5 3, 037001 (2024).

[712] Boris Arseniev, Dmitry Guskov, Richik Sengupta, Jacob Biamonte, and Igor Zacharov, "Tridiagonal matrix decomposition for Hamiltonian simulation on a quantum computer", Physical Review A 109 5, 052629 (2024).

[713] Danial Motlagh and Nathan Wiebe, "Generalized Quantum Signal Processing", PRX Quantum 5 2, 020368 (2024).

[714] Etienne Granet and Henrik Dreyer, "Hamiltonian dynamics on digital quantum computers without discretization error", npj Quantum Information 10 1, 82 (2024).

[715] Zohreh Davoudi, Alexander F. Shaw, and Jesse R. Stryker, "General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory", Quantum 7, 1213 (2023).

[716] Yuval R. Sanders, Dominic W. Berry, Pedro C.S. Costa, Louis W. Tessler, Nathan Wiebe, Craig Gidney, Hartmut Neven, and Ryan Babbush, "Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization", PRX Quantum 1 2, 020312 (2020).

[717] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, "Time-dependent Hamiltonian simulation withL1-norm scaling", Quantum 4, 254 (2020).

[718] Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, and Artur F Izmaylov, "Reducing molecular electronic Hamiltonian simulation cost for linear combination of unitaries approaches", Quantum Science and Technology 8 3, 035019 (2023).

[719] Yasunari Suzuki, Suguru Endo, Keisuke Fujii, and Yuuki Tokunaga, "Quantum Error Mitigation as a Universal Error Reduction Technique: Applications from the NISQ to the Fault-Tolerant Quantum Computing Eras", PRX Quantum 3 1, 010345 (2022).

[720] Shi-Jie Pan, Lin-Chun Wan, Hai-Ling Liu, Qing-Le Wang, Su-Juan Qin, Qiao-Yan Wen, and Fei Gao, "Improved quantum algorithm for A-optimal projection", Physical Review A 102 5, 052402 (2020).

[721] Anthony Ciavarella, "Algorithm for quantum computation of particle decays", Physical Review D 102 9, 094505 (2020).

[722] Grecia Castelazo, Quynh T. Nguyen, Giacomo De Palma, Dirk Englund, Seth Lloyd, and Bobak T. Kiani, "Quantum algorithms for group convolution, cross-correlation, and equivariant transformations", Physical Review A 106 3, 032402 (2022).

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[724] Kazuki Sakamoto and Keisuke Fujii, "On the quantum computational complexity of classical linear dynamics with geometrically local interactions: Dequantization and universality", Quantum 10, 2182 (2026).

[725] Andrew D. King, Alberto Nocera, Marek M. Rams, Jacek Dziarmaga, Roeland Wiersema, William Bernoudy, Jack Raymond, Nitin Kaushal, Niclas Heinsdorf, Richard Harris, Kelly Boothby, Fabio Altomare, Mohsen Asad, Andrew J. Berkley, Martin Boschnak, Kevin Chern, Holly Christiani, Samantha Cibere, Jake Connor, Martin H. Dehn, Rahul Deshpande, Sara Ejtemaee, Pau Farre, Kelsey Hamer, Emile Hoskinson, Shuiyuan Huang, Mark W. Johnson, Samuel Kortas, Eric Ladizinsky, Trevor Lanting, Tony Lai, Ryan Li, Allison J. R. MacDonald, Gaelen Marsden, Catherine C. McGeoch, Reza Molavi, Travis Oh, Richard Neufeld, Mana Norouzpour, Joel Pasvolsky, Patrick Poitras, Gabriel Poulin-Lamarre, Thomas Prescott, Mauricio Reis, Chris Rich, Mohammad Samani, Benjamin Sheldan, Anatoly Smirnov, Edward Sterpka, Berta Trullas Clavera, Nicholas Tsai, Mark Volkmann, Alexander M. Whiticar, Jed D. Whittaker, Warren Wilkinson, Jason Yao, T. J. Yi, Anders W. Sandvik, Gonzalo Alvarez, Roger G. Melko, Juan Carrasquilla, Marcel Franz, and Mohammad H. Amin, "Beyond-classical computation in quantum simulation", Science 388 6743, 199 (2025).

[726] Guang Hao Low, Robbie King, Dominic W. Berry, Qiushi Han, A. Eugene DePrince, Alec F. White, Ryan Babbush, Rolando D. Somma, and Nicholas C. Rubin, "Fast Quantum Simulation of Electronic Structure by Spectral Amplification", Physical Review X 15 4, 041016 (2025).

[727] Kevin J. Joven, Elin Ranjan Das, Joel Bierman, Aishwarya Majumdar, Masoud Hakimi Heris, and Yuan Liu, "Scalable quantum computational science: A perspective from block-encodings and polynomial transformations", APL Computational Physics 2 1, 010901 (2026).

[728] Mohsen Bagherimehrab, Luis Mantilla Calderón, Dominic W. Berry, Philipp Schleich, Mohammad Ghazi Vakili, Abdulrahman Aldossary, Jorge A. Campos Gonzalez Angulo, Christoph Gorgulla, and Alán Aspuru-Guzik, "Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas", PRX Quantum 7 3, 033018 (2026).

[729] Kaoru Mizuta and Tomotaka Kuwahara, "Trotterization is Substantially Efficient for Low-Energy States", Physical Review Letters 135 13, 130602 (2025).

[730] Ethan Decker, Lucas Goetz, Evan McKinney, Erik Gustafson, Junyu Zhou, Yuhao Liu, Alex K. Jones, Ang Li, Alexander Schuckert, Samuel Stein, Eleanor Crane, and Gushu Li, 2026 ACM/IEEE 53rd Annual International Symposium on Computer Architecture (ISCA) 905 (2026) ISBN:979-8-3315-5065-3.

[731] Yong-Mei Li, Hai-Ling Liu, Shi-Jie Pan, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen, "General quantum matrix exponential dimensionality-reduction framework based on block encoding", Physical Review A 108 4, 042418 (2023).

[732] Lindsay Bassman Oftelie, Miroslav Urbanek, Mekena Metcalf, Jonathan Carter, Alexander F Kemper, and Wibe A de Jong, "Simulating quantum materials with digital quantum computers", Quantum Science and Technology 6 4, 043002 (2021).

[733] Lin Lin and Yu Tong, "Near-optimal ground state preparation", Quantum 4, 372 (2020).

[734] Jacob S. Nelson and Andrew D. Baczewski, "Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers", Physical Review A 110 4, 042420 (2024).

[735] Tyler Kharazi, Ahmad M. Alkadri, Jin-Peng Liu, Kranthi K. Mandadapu, and K. Birgitta Whaley, "Explicit block encodings of boundary value problems for many-body elliptic operators", Quantum 9, 1764 (2025).

[736] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Improved Hamiltonians for Quantum Simulations of Gauge Theories", Physical Review Letters 129 5, 051601 (2022).

[737] Junpeng Hu, Shi Jin, Nana Liu, and Lei Zhang, "Quantum random feature method for solving partial differential equations", Discrete and Continuous Dynamical Systems 55, 497 (2026).

[738] Lin Lin and Yu Tong, "Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers", PRX Quantum 3 1, 010318 (2022).

[739] Sahar Ben Rached, Isaac Lopez Agudo, Santiago Rodrigo, Medina Bandic, Artur Garcia-Saez, Sebastian Feld, Hans van Someren, Eduard Alarcón, Carmen G. Almudéver, and Sergi Abadal, "Characterizing the Inter-Core Qubit Traffic in Large-Scale Quantum Modular Architectures", IEEE Access 13, 113236 (2025).

[740] Hai‐Ling Liu, Lin‐Chun Wan, Chao‐Hua Yu, Shi‐Jie Pan, Su‐Juan Qin, Fei Gao, and Qiao‐Yan Wen, "A Quantum Algorithm for Solving Eigenproblem of the Laplacian Matrix of a Fully Connected Weighted Graph", Advanced Quantum Technologies 6 7, 2300031 (2023).

[741] Yasunori Lee and Keita Kanno, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2170 (2025) ISBN:979-8-3315-5736-2.

[742] Rolando D Somma, "Quantum eigenvalue estimation via time series analysis", New Journal of Physics 21 12, 123025 (2019).

[743] Dominic W. Berry, Danial Motlagh, Giacomo Pantaleoni, and Nathan Wiebe, "Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing", Physical Review A 110 1, 012612 (2024).

[744] Xiao-Ming Zhang, Tongyang Li, and Xiao Yuan, "Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications", Physical Review Letters 129 23, 230504 (2022).

[745] William M. Kirby, Sultana Hadi, Michael Kreshchuk, and Peter J. Love, "Quantum simulation of second-quantized Hamiltonians in compact encoding", Physical Review A 104 4, 042607 (2021).

[746] Bo Peng, Yuan Su, Daniel Claudino, Karol Kowalski, Guang Hao Low, and Martin Roetteler, "Quantum simulation of boson-related Hamiltonians: techniques, effective Hamiltonian construction, and error analysis", Quantum Science and Technology 10 2, 023002 (2025).

[747] Hou Lu and Lv Chang, 2024 IEEE International Symposium on Information Theory (ISIT) 2056 (2024) ISBN:979-8-3503-8284-6.

[748] Min-Quan He, Dan-Bo Zhang, and Z. D. Wang, "Quantum Gaussian filter for exploring ground-state properties", Physical Review A 106 3, 032420 (2022).

[749] Muchun Yang, D L Zhou, and Yunpeng Zi, "Quantum topological analysis on digraphs", Quantum Science and Technology 11 4, 045022 (2026).

[750] Joseph Peetz, Scott E. Smart, and Prineha Narang, "Quantum simulation via stochastic combination of unitaries", npj Quantum Information 12 1, 52 (2026).

[751] Alessandro Roggero, Chenyi Gu, Alessandro Baroni, and Thomas Papenbrock, "Preparation of excited states for nuclear dynamics on a quantum computer", Physical Review C 102 6, 064624 (2020).

[752] Benchi Zhao and Keisuke Fujii, "Variational quantum Hamiltonian engineering", Physical Review Research 7 2, 023123 (2025).

[753] Paul Beame, Niels Kornerup, and Michael Whitmeyer, Proceedings of the 56th Annual ACM Symposium on Theory of Computing 596 (2024) ISBN:9798400703836.

[754] M. Sohaib Alam, Stuart Hadfield, Henry Lamm, and Andy C. Y. Li, "Primitive quantum gates for dihedral gauge theories", Physical Review D 105 11, 114501 (2022).

[755] Chien-Hung Cho, Dominic W. Berry, and Min-Hsiu Hsieh, "Doubling the order of approximation via the randomized product formula", Physical Review A 109 6, 062431 (2024).

[756] Riley W. Chien, Sha Xue, Tarini S. Hardikar, Kanav Setia, and James D. Whitfield, "Analysis of superfast encoding performance for electronic structure simulations", Physical Review A 100 3, 032337 (2019).

[757] Kiichiro Toyoizumi, Naoki Yamamoto, and Kazuo Hoshino, "Hamiltonian simulation using the quantum singular-value transformation: Complexity analysis and application to the linearized Vlasov-Poisson equation", Physical Review A 109 1, 012430 (2024).

[758] Chun-Tse Li and Hao-Chung Cheng, "Adaptive circuit learning of born machine: towards realization of amplitude embedding and quantum data loading", Quantum Science and Technology 10 2, 025019 (2025).

[759] Muqing Zheng, Chenxu Liu, Samuel Stein, Xiangyu Li, Johannes Mülmenstädt, Yousu Chen, and Ang Li, "An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications", Algorithms 18 8, 491 (2025).

[760] "Implémentation, analyse et améliorations bas-niveau d'algorithmes quantiques pour le calcul scientifique", Université de Montpellier (2022-....) (2022).

[761] Samuel Jaques and Arthur G. Rattew, "QRAM: A Survey and Critique", Quantum 9, 1922 (2025).

[762] Wooseop Hwang and Bálint Koczor, "Preparing ground and excited states using adiabatic CoVaR", New Journal of Physics 27 2, 023025 (2025).

[763] Rei Sakuma, Kaito Wada, Shu Kanno, Kimberlee Keithley, Kenji Sugisaki, Takashi Abe, Hajime Nakamura, and Naoki Yamamoto, "Quantum-phase-estimation-based filtering: Performance analysis and application to low-energy spectral calculations", Physical Review A 113 1, 012602 (2026).

[764] I. Novikau, I.Y. Dodin, and E.A. Startsev, "Simulation of Linear Non-Hermitian Boundary-Value Problems with Quantum Singular-Value Transformation", Physical Review Applied 19 5, 054012 (2023).

[765] Zane M. Rossi, Jeffery Yu, Isaac L. Chuang, and Sho Sugiura, "Quantum advantage for noisy channel discrimination", Physical Review A 105 3, 032401 (2022).

[766] Moody Chu, "Preparing Hamiltonians for quantum simulation: A computational framework for Cartan decomposition via Lax dynamics", Mathematics of Computation 94 356, 2867 (2025).

[767] Alexis Ralli, Tim Weaving, Andrew Tranter, William M. Kirby, Peter J. Love, and Peter V. Coveney, "Unitary partitioning and the contextual subspace variational quantum eigensolver", Physical Review Research 5 1, 013095 (2023).

[768] Matthew Thibodeau and Bryan K. Clark, "Nearly-frustration-free ground state preparation", Quantum 7, 1084 (2023).

[769] Yulong Dong, Lin Lin, Hongkang Ni, and Jiasu Wang, "Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes", SIAM Journal on Scientific Computing 46 5, A2951 (2024).

[770] E. Dinesh Kumar and Steven H. Frankel, "Quantum unitary matrix representation of the lattice Boltzmann model for low Reynolds fluid flow simulation", AVS Quantum Science 7 1, 013802 (2025).

[771] Qisheng Wang, Ji Guan, Junyi Liu, Zhicheng Zhang, and Mingsheng Ying, "New Quantum Algorithms for Computing Quantum Entropies and Distances", IEEE Transactions on Information Theory 70 8, 5653 (2024).

[772] Jacob Bringewatt and Zohreh Davoudi, "Parallelization techniques for quantum simulation of fermionic systems", Quantum 7, 975 (2023).

[773] Youle Wang and Yu Luo, "Resource-efficient quantum principal component analysis", Quantum Science and Technology 9 3, 035031 (2024).

[774] Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, Marc Gerritsma, and Roeland De Breuker, "Review and perspectives in quantum computing for partial differential equations in structural mechanics", Frontiers in Mechanical Engineering 8, 914241 (2022).

[775] Andrew M. Childs, Jiaqi Leng, Tongyang Li, Jin-Peng Liu, and Chenyi Zhang, "Quantum simulation of real-space dynamics", Quantum 6, 860 (2022).

[776] Matthew B. Hastings, "Classical and Quantum Algorithms for Tensor Principal Component Analysis", Quantum 4, 237 (2020).

[777] Niccoló Fonio, Pierre Sagaut, and Giuseppe Di Molfetta, "Two-dimensional quantum-lattice-gas algorithm for anisotropic Burger-like equations", Physical Review A 114 3, 032426 (2026).

[778] Michael P Kaicher, Simon B Jäger, and Frank K Wilhelm, "Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer", Journal of Physics A: Mathematical and Theoretical 54 39, 395303 (2021).

[779] Javier Argüello-Luengo, Tao Shi, and Alejandro González-Tudela, "Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices", Physical Review A 103 4, 043318 (2021).

[780] Mostafizur Rahaman Laskar and Amit Kumar Dutta, "A Proposed Quantum Framework for Low-Complexity Quantum Simulation and Spectrum Estimation of Hankel-Patterned Systems", IEEE Transactions on Quantum Engineering 4, 1 (2023).

[781] Dong An, Di Fang, and Lin Lin, "Time-dependent unbounded Hamiltonian simulation with vector norm scaling", Quantum 5, 459 (2021).

[782] Andrew Zhao, Andrew Tranter, William M. Kirby, Shu Fay Ung, Akimasa Miyake, and Peter J. Love, "Measurement reduction in variational quantum algorithms", Physical Review A 101 6, 062322 (2020).

[783] Marcello Benedetti, Ansis Rosmanis, and Matthias Rosenkranz, "Probabilistic quantum algorithm for Lyapunov equations and matrix inversion", Physical Review Applied 25 4, 044040 (2026).

[784] Ying Liu, "Grover’s Model with Single Oracle Call and Log(<i>N</i>) Different Diffusion Calls", Journal of Quantum Information Science 16 02, 240 (2026).

[785] Takanori Nishi and Kaoru Yamanouchi, "Simulation of a spin-boson model by iterative optimization of a parametrized quantum circuit", AVS Quantum Science 6 2, 023801 (2024).

[786] Sven Danz, Tobias Stollenwerk, and Alessandro Ciani, "An Implementation of Quantum Oracles for the Finite Element Method", SIAM Journal on Scientific Computing 48 3, B386 (2026).

[787] Xiang Li, Su-Xiang Lyu, Yao Wang, Rui-Xue Xu, Xiao Zheng, and YiJing Yan, "Toward quantum simulation of non-Markovian open quantum dynamics: A universal and compact theory", Physical Review A 110 3, 032620 (2024).

[788] Michal Szczepanik and Emil Zak, "Utilizing redundancies in qubit Hilbert space to reduce entangling gate counts in the unitary vibrational coupled-cluster method", The Journal of Chemical Physics 163 2, 024128 (2025).

[789] Daniel Volya and Prabhat Mishra, 2021 58th ACM/IEEE Design Automation Conference (DAC) 463 (2021) ISBN:978-1-6654-3274-0.

[790] Sivaprasad Omanakuttan and T. J. Volkoff, "Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles", Physical Review A 108 2, 022428 (2023).

[791] Jack S. Baker, Pablo A. M. Casares, Modjtaba Shokrian Zini, Jaydeep Thik, Debasish Banerjee, Chen Ling, Alain Delgado, and Juan Miguel Arrazola, "Simulating optically active spin defects with a quantum computer", Physical Review A 110 3, 032606 (2024).

[792] Zachary P. Bradshaw, Margarite L. LaBorde, and Mark M. Wilde, "Cycle index polynomials and generalized quantum separability tests", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479 2274, 20220733 (2023).

[793] Steven Herbert, Quantum Computing (2026) ISBN:9780191964381.

[794] Zane M. Rossi and Isaac L. Chuang, "Semantic embedding for quantum algorithms", Journal of Mathematical Physics 64 12, 122202 (2023).

[795] Langyu Li, "Principal Trotter observation error with truncated commutators", Physical Review A 110 6, 062614 (2024).

[796] Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, and Tamás Terlaky, "Efficient Use of Quantum Linear System Algorithms in Inexact Infeasible IPMs for Linear Optimization", Journal of Optimization Theory and Applications 202 1, 146 (2024).

[797] Alan C. Santos, "Validity condition for high-fidelity digitized quantum annealing", Physical Review A 111 2, 022618 (2025).

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[799] Mengbo Yan, Dabo Zhang, Kanghai Yang, and Yuan Cao, "A Quantum Computing Method for AC Power Flow with Residual-Controlled Dynamic Precision", Entropy 28 9, 988 (2026).

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[802] Rolando D. Somma, Robbie King, Robin Kothari, Thomas E. O’Brien, and Ryan Babbush, "Shadow hamiltonian simulation", Nature Communications 16 1, 2690 (2025).

[803] Wenyang Qian, Meijian Li, Carlos A. Salgado, and Michael Kreshchuk, "Efficient quantum simulation of QCD jets on the light front", Physical Review D 111 9, 096001 (2025).

[804] Mahmoud Mahdian and H. Davoodi Yeganeh, "Incoherent quantum algorithm dynamics of an open system with near-term devices", Quantum Information Processing 19 9, 285 (2020).

[805] Jason Iaconis, Sonika Johri, and Elton Yechao Zhu, "Quantum state preparation of normal distributions using matrix product states", npj Quantum Information 10 1, 15 (2024).

[806] John M. Martyn and Patrick Rall, "Halving the cost of quantum algorithms with randomization", npj Quantum Information 11 1, 47 (2025).

[807] Bo Peng and Karol Kowalski, "Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of nonunitary operators", Physical Review Research 4 4, 043172 (2022).

[808] Nick S. Blunt, György P. Gehér, and Alexandra E. Moylett, "Compilation of a simple chemistry application to quantum error correction primitives", Physical Review Research 6 1, 013325 (2024).

[809] Yupan Liu and Qisheng Wang, "On Estimating the Trace of Quantum State Powers", IEEE Transactions on Information Theory 72 8, 5830 (2026).

[810] Yulong Dong, Lin Lin, and Yu Tong, "Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices", PRX Quantum 3 4, 040305 (2022).

[811] Yingkai Ouyang, David R. White, and Earl T. Campbell, "Compilation by stochastic Hamiltonian sparsification", Quantum 4, 235 (2020).

[812] Shu Kanno, Takao Kobayashi, Kimberlee Keithley, and Qi Gao, "Resource Estimates for Excited-State Calculations of Diarylethenes on Fault-Tolerant Photonic Quantum Computers", ACS Omega acsomega.4c09568 (2025).

[813] Luca Pennati, Erik M. Åsgrim, Jeremy J. Williams, Stefan Costea, David Tskhakaya, Leon Kos, Ales Podolnik, Yi Ju, Tapish Narwal, Julian Lenz, Michael Bussmann, Urs Ganse, Minna Palmroth, Kallia Chronaki, Vassilis Papaefstathiou, Etienne Renault, Felix Jung, Martin Schulz, Valentin Seitz, Marta Garcia-Gasulla, Filippo Mantovani, Frank Jenko, Erwin Laure, and Stefano Markidis, Proceedings of the 40th ACM International Conference on Supercomputing - Workshops 133 (2026) ISBN:9798400723001.

[814] Mason L. Rhodes, Michael Kreshchuk, and Shivesh Pathak, "Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques", PRX Quantum 5 4, 040347 (2024).

[815] Tianfeng Feng, Yue Cao, Wenjun Yu, Junkai Zeng, Xiaopeng Li, Xiu-Hao Deng, and Qi Zhao, "Entanglement-induced resilience of quantum dynamics", Science Advances 12 40, eaef3416 (2026).

[816] Zohreh Davoudi, Norbert M. Linke, and Guido Pagano, "Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach", Physical Review Research 3 4, 043072 (2021).

[817] Yuki Ito, Hitomi Mori, Kazuki Sakamoto, and Keisuke Fujii, "Polynomial time constructive decision algorithm for multivariable quantum signal processing", Quantum 10, 2102 (2026).

[818] Christopher F. Kane, Niladri Gomes, and Michael Kreshchuk, "Nearly optimal state preparation for quantum simulations of lattice gauge theories", Physical Review A 110 1, 012455 (2024).

[819] Jeongwan Haah, Matthew B. Hastings, Robin Kothari, and Guang Hao Low, "Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians", SIAM Journal on Computing 52 6, FOCS18-250 (2023).

[820] XingAo Liu, Ri-Gui Zhou, WenYu Guo, XiaoRong You, and Jia Luo, "Quantum Algorithm for Classical Multidimensional Scaling", International Journal of Theoretical Physics 63 7, 162 (2024).

[821] César Feniou, Olivier Adjoua, Baptiste Claudon, Julien Zylberman, Emmanuel Giner, and Jean-Philip Piquemal, "Sparse Quantum State Preparation for Strongly Correlated Systems", The Journal of Physical Chemistry Letters 15 11, 3197 (2024).

[822] Mark Steudtner and Stephanie Wehner, "Estimating exact energies in quantum simulation without Toffoli gates", Physical Review A 101 5, 052329 (2020).

[823] Benedikt Fauseweh and Jian-Xin Zhu, "Quantum computing Floquet energy spectra", Quantum 7, 1063 (2023).

[824] Yukun Zhang, Xiaoming Zhang, Jinzhao Sun, Heng Lin, Yifei Huang, Dingshun Lv, and Xiao Yuan, "Quantum Algorithms for Quantum Molecular Systems: A Survey", WIREs Computational Molecular Science 15 3, e70020 (2025).

[825] Alicja Dutkiewicz, Stefano Polla, Maximilian Scheurer, Christian Gogolin, William J. Huggins, and Thomas E. O’Brien, "Error Mitigation and Circuit Division for Early Fault-Tolerant Quantum Phase Estimation", PRX Quantum 6 4, 040318 (2025).

[826] Stefano Polla, Gian-Luca R. Anselmetti, and Thomas E. O'Brien, "Optimizing the information extracted by a single qubit measurement", Physical Review A 108 1, 012403 (2023).

[827] Xiantao Li, "Some error analysis for the quantum phase estimation algorithms", Journal of Physics A: Mathematical and Theoretical 55 32, 325303 (2022).

[828] Alexey Pyrkov, Alex Aliper, Dmitry Bezrukov, and Alex Zhavoronkov, Applied Artificial Intelligence for Drug Discovery 289 (2026) ISBN:978-3-031-98021-3.

[829] Bojko N. Bakalov, João C. Getelina, Raghav G. Jha, Alexander F. Kemper, and Yuan Liu, "Quantum simulation of massive Thirring and Gross-Neveu models for arbitrary number of flavors", Physical Review D 113 11, 114508 (2026).

[830] Sofiene Jerbi, Lea M. Trenkwalder, Hendrik Poulsen Nautrup, Hans J. Briegel, and Vedran Dunjko, "Quantum Enhancements for Deep Reinforcement Learning in Large Spaces", PRX Quantum 2 1, 010328 (2021).

[831] Luning Zhao, Joshua Goings, Kyujin Shin, Woomin Kyoung, Johanna I. Fuks, June-Koo Kevin Rhee, Young Min Rhee, Kenneth Wright, Jason Nguyen, Jungsang Kim, and Sonika Johri, "Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers", npj Quantum Information 9 1, 60 (2023).

[832] Qi Zhao, You Zhou, Alexander F. Shaw, Tongyang Li, and Andrew M. Childs, "Hamiltonian Simulation with Random Inputs", Physical Review Letters 129 27, 270502 (2022).

[833] Samuel Jaques and Thomas Häner, "Leveraging State Sparsity for More Efficient Quantum Simulations", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[834] Changpeng Shao, "Quantum speedup of Bayes’ classifiers", Journal of Physics A: Mathematical and Theoretical 53 4, 045301 (2020).

[835] Xiaoming Sun, Guojing Tian, Shuai Yang, Pei Yuan, and Shengyu Zhang, "Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 42 10, 3301 (2023).

[836] Athena Caesura, Cristian L. Cortes, William Pol, Sukin Sim, Mark Steudtner, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif, and Christofer S. Tautermann, "Faster Quantum Chemistry Simulations on a Quantum Computer with Improved Tensor Factorization and Active Volume Compilation", PRX Quantum 6 3, 030337 (2025).

[837] Guoqing Zhou, Lihuang Qian, and Paolo Gamba, "A Novel Iterative Self-Organizing Pixel Matrix Entanglement Classifier for Remote Sensing Imagery", IEEE Transactions on Geoscience and Remote Sensing 62, 1 (2024).

[838] Juan M. Gimenez, Fehmi Cirak, and Michael Ortiz, "A quantum spectral solver for periodic incompressible Stokes flow", Computer Methods in Applied Mechanics and Engineering 463, 119453 (2027).

[839] Qing-Song Li, Huan-Yu Liu, Qingchun Wang, Yu-Chun Wu, and Guo-Ping Guo, "Huffman-Code-Based Ternary Tree Transformation", Chinese Physics Letters 42 10, 100001 (2025).

[840] Hongxiang Chen, Max Nusspickel, Jules Tilly, and George H. Booth, "Variational quantum eigensolver for dynamic correlation functions", Physical Review A 104 3, 032405 (2021).

[841] Max Bee-Lindgren, Zhengrong Qian, Matthew DeCross, Natalie C. Brown, Christopher N. Gilbreth, Jacob Watkins, Xilin Zhang, and Dean Lee, "Controlled gate networks: theory and application to eigenvalue estimation", The European Physical Journal A 61 11, 263 (2025).

[842] Christopher F. Kane, Siddharth Hariprakash, Neel S. Modi, Michael Kreshchuk, and Christian W Bauer, "Block encoding bosons by signal processing", Quantum 9, 1747 (2025).

[843] Patrick Rall, "Quantum algorithms for estimating physical quantities using block encodings", Physical Review A 102 2, 022408 (2020).

[844] Guang Hao Low and Yuan Su, "Quantum Eigenvalue Processing", SIAM Journal on Computing 55 1, 135 (2026).

[845] Nishchay Suri, Joseph Barreto, Stuart Hadfield, Nathan Wiebe, Filip Wudarski, and Jeffrey Marshall, "Two-Unitary Decomposition Algorithm and Open Quantum System Simulation", Quantum 7, 1002 (2023).

[846] Thomas E. Baker, "Block Lanczos method for excited states on a quantum computer", Physical Review A 110 1, 012420 (2024).

[847] Trevor Keen, Bo Peng, Karol Kowalski, Pavel Lougovski, and Steven Johnston, "Hybrid quantum-classical approach for coupled-cluster Green's function theory", Quantum 6, 675 (2022).

[848] Aaron Miller, Adam Glos, and Zoltán Zimborás, "Treespilation: architecture- and state-optimised fermion-to-qubit mappings", npj Quantum Information 12 1, 26 (2026).

[849] Zohreh Davoudi, "Toward quantum computing gauge theories of nature", The European Physical Journal Special Topics 235 17, 3847 (2026).

[850] Evan Borras and Milad Marvian, "Quantum simulation algorithms based on quantum trajectories", Quantum 10, 2063 (2026).

[851] Keisuke Murota and Takumi Kobori, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 1536 (2025) ISBN:979-8-3315-5736-2.

[852] Yudong Cao, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Mária Kieferová, Ian D. Kivlichan, Tim Menke, Borja Peropadre, Nicolas P. D. Sawaya, Sukin Sim, Libor Veis, and Alán Aspuru-Guzik, "Quantum Chemistry in the Age of Quantum Computing", Chemical Reviews 119 19, 10856 (2019).

[853] John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang, "Grand Unification of Quantum Algorithms", PRX Quantum 2 4, 040203 (2021).

[854] Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", Quantum 3, 128 (2019).

[855] Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, and Yuan Su, "Toward the first quantum simulation with quantum speedup", Proceedings of the National Academy of Science 115 38, 9456 (2018).

[856] Earl Campbell, "Random Compiler for Fast Hamiltonian Simulation", Physical Review Letters 123 7, 070503 (2019).

[857] Vedran Dunjko and Hans J. Briegel, "Machine learning & artificial intelligence in the quantum domain: a review of recent progress", Reports on Progress in Physics 81 7, 074001 (2018).

[858] Ryan Babbush, Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, and Garnet Kin-Lic Chan, "Low-Depth Quantum Simulation of Materials", Physical Review X 8 1, 011044 (2018).

[859] Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven, "Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity", Physical Review X 8 4, 041015 (2018).

[860] Dominic W. Berry, Andrew M. Childs, Aaron Ostrander, and Guoming Wang, "Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision", Communications in Mathematical Physics 356 3, 1057 (2017).

[861] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe, "Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics", arXiv:1806.01838, (2018).

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[934] Qisheng Wang and Zhicheng Zhang, "Quantum Lower Bounds by Sample-to-Query Lifting", arXiv:2308.01794, (2023).

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[942] Qisheng Wang and Zhicheng Zhang, "Fast Quantum Algorithms for Trace Distance Estimation", arXiv:2301.06783, (2023).

[943] François Le Gall, Yupan Liu, and Qisheng Wang, "Space-bounded quantum state testing via space-efficient quantum singular value transformation", arXiv:2308.05079, (2023).

[944] Yuki Ito, Yu Tanaka, and Keisuke Fujii, "How to Map Linear Differential Equations to Schrödinger Equations via Carleman and Koopman-von Neumann Embeddings for Quantum Algorithms", arXiv:2311.15628, (2023).

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[946] Lorenzo Laneve, "Robust black-box quantum-state preparation via quantum signal processing", arXiv:2305.04705, (2023).

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[952] Lorenzo Laneve, "Quantum Signal Processing, Phase Extraction, and Proportional Sampling", arXiv:2303.11077, (2023).

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[957] Lewis W. Anderson, Martin Kiffner, Tom O'Leary, Jason Crain, and Dieter Jaksch, "Solving lattice gauge theories using the quantum Krylov algorithm and qubitization", arXiv:2403.08859, (2024).

[958] Lvzhou Li and Jingquan Luo, "Nearly Optimal Circuit Size for Sparse Quantum State Preparation", arXiv:2406.16142, (2024).

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[963] Osama Muhammad Raisuddin and Suvranu De, "A Review of Quantum Scientific Computing Algorithms for Engineering Problems", arXiv:2408.13943, (2024).

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[965] Aleksei V. Ivanov, Andrew Patterson, Marius Bothe, Christoph Sünderhauf, Bjorn K. Berntson, Jens Jørgen Mortensen, Mikael Kuisma, Earl Campbell, and Róbert Izsák, "Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set", arXiv:2408.03159, (2024).

[966] Zhenning Liu, Xiantao Li, Chunhao Wang, and Jin-Peng Liu, "Toward end-to-end quantum simulation for protein dynamics", arXiv:2411.03972, (2024).

[967] Thomas W. Watts, Matthew Otten, Jason T. Necaise, Nam Nguyen, Benjamin Link, Kristen S. Williams, Yuval R. Sanders, Samuel J. Elman, Maria Kieferova, Michael J. Bremner, Kaitlyn J. Morrell, Justin E. Elenewski, Samuel D. Johnson, Luke Mathieson, Kevin M. Obenland, Rashmi Sundareswara, and Adam Holmes, "Prospects for Quantum Computation in Propellant Design: Assessing the Stability of Cyclic Ozone in Nanoscale Confinement", arXiv:2408.13244, (2024).

[968] L. Spagnoli, A. Roggero, and N. Wiebe, "Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes", arXiv:2405.19293, (2024).

[969] Tyler Kharazi, Torin F. Stetina, Liwen Ko, Guang Hao Low, and K. Birgitta Whaley, "An efficient quantum algorithm for generation of ab initio n-th order susceptibilities for non-linear spectroscopies", arXiv:2404.01454, (2024).

[970] Tianfeng Feng, Jue Xu, Wenjun Yu, Zekun Ye, Penghui Yao, and Qi Zhao, "Distributed Quantum Simulation", arXiv:2411.02881, (2024).

[971] Yuki Ito, Hitomi Mori, Kazuki Sakamoto, and Keisuke Fujii, "Polynomial time constructive decision algorithm for multivariable quantum signal processing", arXiv:2410.02332, (2024).

[972] Yanlin Chen, András Gilyén, and Ronald de Wolf, "A Quantum Speed-Up for Approximating the Top Eigenvectors of a Matrix", arXiv:2405.14765, (2024).

[973] Mohsen Bagherimehrab, Luis Mantilla Calderon, Dominic W. Berry, Philipp Schleich, Mohammad Ghazi Vakili, Abdulrahman Aldossary, Jorge A. Campos Gonzalez Angulo, Christoph Gorgulla, and Alan Aspuru-Guzik, "Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas", arXiv:2409.08265, (2024).

[974] Merel A. Schalkers and Matthias Möller, "Efficient and fail-safe quantum algorithm for the transport equation", Journal of Computational Physics 502, 112816 (2024).

[975] Ivan Novikau and Ilon Joseph, "Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems", arXiv:2410.03985, (2024).

[976] Qisheng Wang and Zhicheng Zhang, "Time-Efficient Quantum Entropy Estimator via Samplizer", arXiv:2401.09947, (2024).

[977] Weijun Feng, Gongde Guo, Song Lin, and Yongzhen Xu, "Quantum Isomap algorithm for manifold learning", Physical Review Applied 22 1, 014049 (2024).

[978] Hari Krovi, "Quantum algorithms to simulate quadratic classical Hamiltonians and optimal control", arXiv:2404.07303, (2024).

[979] Julien Gacon, "Scalable Quantum Algorithms for Noisy Quantum Computers", arXiv:2403.00940, (2024).

[980] Pau Escofet, Anabel Ovide, Medina Bandic, Luise Prielinger, Hans van Someren, Sebastian Feld, Eduard Alarcón, Sergi Abadal, and Carmen G. Almudéver, "Revisiting the Mapping of Quantum Circuits: Entering the Multi-Core Era", arXiv:2403.17205, (2024).

[981] S. E. Skelton, "Mostly Harmless Methods for QSP-Processing with Laurent Polynomials", arXiv:2408.04321, (2024).

[982] Tae-Won Kim and Byung-Soo Choi, "Dequantizability from inputs", arXiv:2405.13273, (2024).

[983] Chusei Kiumi, Yohei Tanaka, and Akito Suzuki, "Operator quantum singular value transformation: Spectral mapping, design and topological invariants", arXiv:2401.09007, (2024).

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[985] Adelina Bärligea, Benedikt Poggel, and Jeanette Miriam Lorenz, "Solving Combinatorial Optimization Problems with a Block Encoding Quantum Optimizer", arXiv:2404.14054, (2024).

[986] Yizhi Shen, Niel Van Buggenhout, Daan Camps, Katherine Klymko, and Roel Van Beeumen, "Quantum Rational Transformation Using Linear Combinations of Hamiltonian Simulations", arXiv:2408.07742, (2024).

[987] Hefeng Wang and Hua Xiang, "Quantum optimization algorithm based on multistep quantum computation", New Journal of Physics 26 7, 073031 (2024).

[988] Ichio Kikuchi and Akihito Kikuchi, "Feasibility of first principles molecular dynamics in fault-tolerant quantum computer by quantum phase estimation", arXiv:2404.10001, (2024).

[989] Guojian Wu, Fang Gao, Qing Gao, and Yu Pan, "Quantum Discrete Adiabatic Linear Solver based on Block Encoding and Eigenvalue Separator", arXiv:2412.06202, (2024).

[990] Minbo Gao, Zhengfeng Ji, and Qisheng Wang, "Quantum Approximate $k$-Minimum Finding", arXiv:2412.16586, (2024).

[991] Zohreh Davoudi, Chung-Chun Hsieh, and Saurabh V. Kadam, "Quantum computation of hadron scattering in a lattice gauge theory", arXiv:2505.20408, (2025).

[992] James Ingoldby, Michael Spannowsky, Timur Sypchenko, Simon Williams, and Matthew Wingate, "Real-Time Scattering on Quantum Computers via Hamiltonian Truncation", arXiv:2505.03878, (2025).

[993] Shantanav Chakraborty, Soumyabrata Hazra, Tongyang Li, Changpeng Shao, Xinzhao Wang, and Yuxin Zhang, "Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla", arXiv:2504.02385, (2025).

[994] Daan Camps, Ermal Rrapaj, Katherine Klymko, Hyeongjin Kim, Kevin Gott, Siva Darbha, Jan Balewski, Brian Austin, and Nicholas J. Wright, "Quantum Computing Technology Roadmaps and Capability Assessment for Scientific Computing -- An analysis of use cases from the NERSC workload", arXiv:2509.09882, (2025).

[995] Ethan Decker, Lucas Goetz, Evan McKinney, Erik Gustafson, Junyu Zhou, Yuhao Liu, Alex K. Jones, Ang Li, Alexander Schuckert, Samuel Stein, Eleanor Crane, and Gushu Li, "Kernpiler: Compiler Optimization for Quantum Hamiltonian Simulation with Partial Trotterization", arXiv:2504.07214, (2025).

[996] Takeru Utsumi, Yoshifumi Nakata, Qisheng Wang, and Ryuji Takagi, "Quantum algorithms for Uhlmann transformation", arXiv:2509.03619, (2025).

[997] Christopher F. Kane, Siddharth Hariprakash, and Christian W. Bauer, "Obtaining continuum physics from dynamical simulations of Hamiltonian lattice gauge theories", arXiv:2506.16559, (2025).

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[999] Sam McArdle, Alexander M. Dalzell, Aleksander Kubica, and Fernando G. S. L. Brandão, "The Fast for the Curious: How to accelerate fault-tolerant quantum applications", arXiv:2510.26078, (2025).

[1000] Nick S. Blunt, Aleksei V. Ivanov, and Andreas Juul Bay-Smidt, "A Monte Carlo approach to bound Trotter error", arXiv:2510.11621, (2025).

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Hamiltonian Simulation by Qubitization

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