Near-optimal ground state preparation

Lin Lin; Yu Tong

doi:10.22331/q-2020-12-14-372

Near-optimal ground state preparation

Lin Lin^1,2 and Yu Tong¹

¹Department of Mathematics, University of California, Berkeley, CA 94720, USA
²Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Published:	2020-12-14, volume 4, page 372
Eprint:	arXiv:2002.12508v3
Doi:	https://doi.org/10.22331/q-2020-12-14-372
Citation:	Quantum 4, 372 (2020).

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Abstract

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

► BibTeX data

@article{Lin2020nearoptimalground,
  doi = {10.22331/q-2020-12-14-372},
  url = {https://doi.org/10.22331/q-2020-12-14-372},
  title = {Near-optimal ground state preparation},
  author = {Lin, Lin and Tong, Yu},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {372},
  month = dec,
  year = {2020}
}

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[71] 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).

[72] Yulong Dong, Lin Lin, Hongkang Ni, and Jiasu Wang, "Infinite quantum signal processing", Quantum 8, 1558 (2024).

[73] Lucas K. Kovalsky, Fernando A. Calderon-Vargas, Matthew D. Grace, Alicia B. Magann, James B. Larsen, Andrew D. Baczewski, and Mohan Sarovar, "Self-Healing of Trotter Error in Digital Adiabatic State Preparation", Physical Review Letters 131 6, 060602 (2023).

[74] J. Wayne Mullinax and Norm M. Tubman, "Large-scale sparse wave function circuit simulator for applications with the variational quantum eigensolver", The Journal of Chemical Physics 162 7, 074114 (2025).

[75] Fan Yang, Dafa Zhao, Chao Wei, Xinyu Chen, Shijie Wei, Hefeng Wang, Guilu Long, and Tao Xin, "A parallel quantum eigensolver for quantum machine learning", New Journal of Physics 26 4, 043011 (2024).

[76] 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).

[77] Yu. Malykhin and K. Ryutin, "Polynomial approximation on disjoint segments and amplification of approximation", Journal of Approximation Theory 298, 106010 (2024).

[78] Cheong Eung Ahn and Gil Young Cho, "Simulation and randomized measurement of topological phase on a trapped-ion quantum computer", Journal of the Korean Physical Society 81 3, 258 (2022).

[79] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, "Nearly tight Trotterization of interacting electrons", Quantum 5, 495 (2021).

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

[81] Hiroki Kuji, Yuta Shingu, Tetsuro Nikuni, Takashi Imoto, Kenji Sugisaki, and Yuichiro Matsuzaki, "Robust phase estimation of the ground-state energy without controlled time evolution on a quantum device", Physical Review A 111 4, 042618 (2025).

[82] Haoya Li, Hongkang Ni, and Lexing Ying, "Adaptive low-depth quantum algorithms for robust multiple-phase estimation", Physical Review A 108 6, 062408 (2023).

[83] Mara Vizzuso, Gianluca Passarelli, Giovanni Cantele, Procolo Lucignano, Xi Chen, and Koushik Paul, "Nonadiabatic self-healing of Trotter errors in digitized counterdiabatic dynamics", Physical Review A 113 6, 062432 (2026).

[84] Guoming Wang, Daniel Stilck França, Gumaro Rendon, and Peter D. Johnson, "Efficient ground-state-energy estimation and certification on early fault-tolerant quantum computers", Physical Review A 111 1, 012426 (2025).

[85] Jinzhao Sun, Pei Zeng, Tom Gur, and M. S. Kim, "High-precision and low-depth quantum algorithm design for eigenstate problems", Science Advances 12 3, eaeb1622 (2026).

[86] 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).

[87] Katerina Gratsea, Chong Sun, and Peter D. Johnson, "Evaluating the efficiency of ground-state-preparation algorithms", Physical Review A 109 4, 042425 (2024).

[88] Rajesh K. Malla, Hiroki Sukeno, Hongye Yu, Tzu-Chieh Wei, Andreas Weichselbaum, and Robert M. Konik, "Feedback-based quantum algorithm inspired by counterdiabatic driving", Physical Review Research 6 4, 043068 (2024).

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

[90] Zhiyan Ding and Lin Lin, "Even Shorter Quantum Circuit for Phase Estimation on Early Fault-Tolerant Quantum Computers with Applications to Ground-State Energy Estimation", PRX Quantum 4 2, 020331 (2023).

[91] Stepan Fomichev, Kasra Hejazi, Modjtaba Shokrian Zini, Matthew Kiser, Joana Fraxanet, Pablo Antonio Moreno Casares, Alain Delgado, Joonsuk Huh, Arne-Christian Voigt, Jonathan E. Mueller, and Juan Miguel Arrazola, "Initial State Preparation for Quantum Chemistry on Quantum Computers", PRX Quantum 5 4, 040339 (2024).

[92] Scott E. Smart and Prineha Narang, "Many-body eigenstates from quantum manifold optimization", Physical Review A 110 5, 052430 (2024).

[93] Yusuke Nishiya, Hirofumi Nishi, Yannick Couzinié, Taichi Kosugi, and Yu-ichiro Matsushita, "First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration", Physical Review A 109 2, 022423 (2024).

[94] F. Turro, A. Roggero, V. Amitrano, P. Luchi, K. A. Wendt, J. L. Dubois, S. Quaglioni, and F. Pederiva, "Imaginary-time propagation on a quantum chip", Physical Review A 105 2, 022440 (2022).

[95] S. Pathak, A. E. Russo, S. K. Seritan, and A. D. Baczewski, "Quantifying T -gate-count improvements for ground-state-energy estimation with near-optimal state preparation", Physical Review A 107 4, L040601 (2023).

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

[97] Yu Tong, Dong An, Nathan Wiebe, and Lin Lin, "Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions", Physical Review A 104 3, 032422 (2021).

[98] Judah F. Unmuth-Yockey, "Metropolis-style random sampling of quantum gates for the estimation of low-energy observables", Physical Review D 105 3, 034515 (2022).

[99] Jia-Cheng Huo, Ling Fan, Ru Zhang, and Cong Cao, "A full-quantum algorithm for solving the exact cover problem via quantum gradient descent iteration", Laser Physics 36 3, 035202 (2026).

[100] Kohei Oshio, Yohichi Suzuki, Kaito Wada, Keigo Hisanaga, Shumpei Uno, and Naoki Yamamoto, "Adaptive measurement strategy for noisy quantum amplitude estimation with variational quantum circuits", Physical Review A 110 6, 062423 (2024).

[101] Hardeep Bassi, Yizhi Shen, Harish S. Bhat, and Roel Van Beeumen, "From noisy observables to accurate ground-state energies: A quantum–classical signal subspace approach with denoising", APL Quantum 2 4, 046103 (2025).

[102] 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).

[103] Natalie Klco and D. H. Beck, "Identification of a natural fieldlike entanglement resource in trapped-ion chains", Physical Review A 109 6, 062419 (2024).

[104] Luke Bell, Yan Wang, Kevin C. Smith, Yuan Liu, Eugene Dumitrescu, and S.M. Girvin, "Co-designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation", PRX Quantum 6 4, 040359 (2025).

[105] Erenay Karacan, Yanbin Chen, and Christian B. Mendl, "Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering", Quantum 9, 1624 (2025).

[106] Qing-Xing Xie, Zidong Lin, Yun-Long Liu, and Yan Zhao, "Beyond VQE and QPE: a noise- and sampling-error-tolerant quantum algorithm with Heisenberg-limited precision", Quantum Information Processing 25 4, 128 (2026).

[107] Jakob Günther, Alberto Baiardi, Markus Reiher, and Matthias Christandl, "More quantum chemistry with fewer qubits", Physical Review Research 6 4, 043021 (2024).

[108] William J. Huggins, Kianna Wan, Jarrod McClean, Thomas E. O’Brien, Nathan Wiebe, and Ryan Babbush, "Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values", Physical Review Letters 129 24, 240501 (2022).

[109] Myeonghwan Seong and Daniel Kyungdeock Park, "Hamiltonian formulations of centroid-based clustering", Frontiers in Physics 13, 1544623 (2025).

[110] 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).

[111] Zhiyan Ding, Haoya Li, Lin Lin, HongKang Ni, Lexing Ying, and Ruizhe Zhang, "Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method", Quantum 8, 1487 (2024).

[112] Rei Sakuma, Shu Kanno, Kenji Sugisaki, Takashi Abe, and Naoki Yamamoto, "Entanglement-assisted phase-estimation algorithm for calculating dynamical response functions", Physical Review A 110 2, 022618 (2024).

[113] Nikhil S. Mande and Ronald de Wolf, "Tight Bounds for Quantum Phase Estimation and Related Problems", Quantum 10, 2140 (2026).

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

[115] Mauro Cainelli, Reo Baba, and Yuki Kurashige, "Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules", Journal of Chemical Theory and Computation acs.jctc.4c00483 (2024).

[116] 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).

[117] Hsin-Yuan Huang, Soonwon Choi, Jarrod R. McClean, and John Preskill, "Vast World of Quantum Advantage", Physical Review X 16 3, 030501 (2026).

[118] Dhruv Gopalakrishnan and Michele Mosca, 2024 IEEE 6th International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications (TPS-ISA) 471 (2024) ISBN:979-8-3503-8674-5.

[119] Kianna Wan, "Exponentially faster implementations of Select(H) for fermionic Hamiltonians", Quantum 5, 380 (2021).

[120] Kosuke Mitarai, Kiichiro Toyoizumi, and Wataru Mizukami, "Perturbation theory with quantum signal processing", Quantum 7, 1000 (2023).

[121] Natalie Klco, Alessandro Roggero, and Martin J Savage, "Standard model physics and the digital quantum revolution: thoughts about the interface", Reports on Progress in Physics 85 6, 064301 (2022).

[122] Harry Buhrman, Sevag Gharibian, Zeph Landau, François Le Gall, Norbert Schuch, and Suguru Tamaki, "Beating the Natural Grover Bound for Low-Energy Estimation and State Preparation", Physical Review Letters 135 3, 030601 (2025).

[123] Weijie Du and James P. Vary, "Multinucleon structure and dynamics via quantum computing", Physical Review A 108 5, 052614 (2023).

[124] Maria-Andreea Filip and Nathan Fitzpatrick, "Beyond asymptotic reasoning: the practicalities of a quantum ground state projector based on the wall-Chebyshev expansion", Quantum Science and Technology 11 1, 015027 (2026).

[125] G. E. L. Pexe, L. A. M. Rattighieri, A. L. Malvezzi, and F. F. Fanchini, "Using a feedback-based quantum algorithm to analyze the critical properties of the ANNNI model without classical optimization", Physical Review B 110 22, 224422 (2024).

[126] 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).

[127] 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).

[128] 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).

[129] Fan Xing, Yan Wei, and Zeyang Liao, "Quantum search in many-body interacting systems with long-range interactions", Physical Review A 109 5, 052435 (2024).

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

[131] Muralikrishnan Gopalakrishnan Meena, Kalyana C. Gottiparthi, Justin G. Lietz, Antigoni Georgiadou, and Eduardo Antonio Coello Pérez, "Solving the Hele–Shaw flow using the Harrow–Hassidim–Lloyd algorithm on superconducting devices: A study of efficiency and challenges", Physics of Fluids 36 10, 101705 (2024).

[132] Dominic W. Berry, Yu Tong, Tanuj Khattar, Alec White, Tae In Kim, Guang Hao Low, Sergio Boixo, Zhiyan Ding, Lin Lin, Seunghoon Lee, Garnet Kin-Lic Chan, Ryan Babbush, and Nicholas C. Rubin, "Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules", PRX Quantum 6 2, 020327 (2025).

[133] Shi Jin, Nana Liu, and Yue Yu, "Quantum Simulation of Partial Differential Equations via Schrödingerization", Physical Review Letters 133 23, 230602 (2024).

[134] Yulong Dong, K. Birgitta Whaley, and Lin Lin, "A quantum hamiltonian simulation benchmark", npj Quantum Information 8 1, 131 (2022).

[135] 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).

[136] Shi Jin and Nana Liu, "Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 2292, 20230370 (2024).

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

[138] Ryan V. Mishmash, Tanvi P. Gujarati, Mario Motta, Huanchen Zhai, Garnet Kin-Lic Chan, and Antonio Mezzacapo, "Hierarchical Clifford Transformations to Reduce Entanglement in Quantum Chemistry Wave Functions", Journal of Chemical Theory and Computation 19 11, 3194 (2023).

[139] Qisheng Wang and Zhicheng Zhang, "Quantum Lower Bounds by Sample-to-Query Lifting", SIAM Journal on Computing 54 5, 1294 (2025).

[140] Koichi Miyamoto and Yuichiro Tada, "Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation", Physical Review Research 7 2, 023251 (2025).

[141] Hirofumi Nishi, Taichi Kosugi, Satoshi Hirose, Tatsuya Okayama, and Yu-ichiro Matsushita, "Logical quantum phase estimation for x-ray absorption spectra", Physical Review Applied 25 3, 034026 (2026).

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

[143] Guoming Wang, Sukin Sim, and Peter D. Johnson, "State Preparation Boosters for Early Fault-Tolerant Quantum Computation", Quantum 6, 829 (2022).

[144] 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).

[145] Yongtao Zhan, Zhiyan Ding, Jakob Huhn, Johnnie Gray, John Preskill, Garnet Kin-Lic Chan, and Lin Lin, "Rapid Quantum Ground State Preparation via Dissipative Dynamics", Physical Review X 16 1, 011004 (2026).

[146] L. Wright, F. Barratt, J. Dborin, G. H. Booth, and A. G. Green, "Automatic post-selection by ancillae thermalization", Physical Review Research 3 3, 033151 (2021).

[147] Zhiyan Ding, Chi-Fang Chen, and Lin Lin, "Single-ancilla ground state preparation via Lindbladians", Physical Review Research 6 3, 033147 (2024).

[148] 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).

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

[150] Marek Gluza, Jeongrak Son, Bi Hong Tiang, René Zander, Raphael Seidel, Yudai Suzuki, Zoë Holmes, and Nelly H. Y. Ng, "Double-Bracket Quantum Algorithms for Quantum Imaginary-Time Evolution", Physical Review Letters 136 2, 020601 (2026).

[151] Jiaqi Leng, Zhiyan Ding, Zherui Chen, and Lin Lin, "Operator-level quantum acceleration of non-logconcave sampling", Proceedings of the National Academy of Sciences 123 8, e2512789123 (2026).

[152] Yongdan Yang, Ying Li, Xiaosi Xu, and Xiao Yuan, "Resource-efficient quantum-classical hybrid algorithm for energy gap evaluation", Physical Review A 109 5, 052416 (2024).

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

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

[155] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "Complexity of Implementing Trotter Steps", PRX Quantum 4 2, 020323 (2023).

[156] Sam McArdle, András Gilyén,, and Mario Berta, "A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits", Quantum 10, 2058 (2026).

[157] Hans Hon Sang Chan, Richard Meister, Tyson Jones, David P. Tew, and Simon C. Benjamin, "Grid-based methods for chemistry simulations on a quantum computer", Science Advances 9 9, eabo7484 (2023).

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

[159] 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).

[160] Takeru Utsumi and Yoshifumi Nakata, "Explicit decoders using fixed-point amplitude amplification based on QSVT", Quantum 10, 2024 (2026).

[161] 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).

[162] Raffaele Santagati, Alan Aspuru-Guzik, Ryan Babbush, Matthias Degroote, Leticia González, Elica Kyoseva, Nikolaj Moll, Markus Oppel, Robert M. Parrish, Nicholas C. Rubin, Michael Streif, Christofer S. Tautermann, Horst Weiss, Nathan Wiebe, and Clemens Utschig-Utschig, "Drug design on quantum computers", Nature Physics 20 4, 549 (2024).

[163] Garnet Kin-Lic Chan, "Spiers Memorial Lecture: Quantum chemistry, classical heuristics, and quantum advantage", Faraday Discussions 254, 11 (2024).

[164] Kai Li, Ming Zhang, Xiaowen Liu, Yong Liu, Hongyi Dai, Yijun Zhang, and Chen Dong, "Quantum Linear System Algorithm for General Matrices in System Identification", Entropy 24 7, 893 (2022).

[165] Jiasu Wang, Yulong Dong, and Lin Lin, "On the energy landscape of symmetric quantum signal processing", Quantum 6, 850 (2022).

[166] Kaoru Mizuta and Keisuke Fujii, "Recursive quantum eigenvalue and singular-value transformation: Analytic construction of matrix sign function by Newton iteration", Physical Review Research 6 1, L012007 (2024).

[167] Gabriel Waite, Karl Lin, Samuel J. Elman, and Michael J. Bremner, "Physically motivated guiding states for local Hamiltonians", Physical Review A 114 1, 012431 (2026).

[168] Thomas E. O'Brien, Michael Streif, Nicholas C. Rubin, Raffaele Santagati, Yuan Su, William J. Huggins, Joshua J. Goings, Nikolaj Moll, Elica Kyoseva, Matthias Degroote, Christofer S. Tautermann, Joonho Lee, Dominic W. Berry, Nathan Wiebe, and Ryan Babbush, "Efficient quantum computation of molecular forces and other energy gradients", Physical Review Research 4 4, 043210 (2022).

[169] A. E. Russo, K. M. Rudinger, B. C. A. Morrison, and A. D. Baczewski, "Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation", Physical Review Letters 126 21, 210501 (2021).

[170] Gabriel Greene-Diniz, David Zsolt Manrique, Kentaro Yamamoto, Evgeny Plekhanov, Nathan Fitzpatrick, Michal Krompiec, Rei Sakuma, and David Muñoz Ramo, "Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method", Quantum 8, 1383 (2024).

[171] Weijie Du, Yangguang Yang, Zixin Liu, Chao Yang, and James P. Vary, "Quantum-classical computational framework for many-fermion response and structure", Physics Letters B 878, 140538 (2026).

[172] 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).

[173] Allan Tosta, Thais de Lima Silva, Giancarlo Camilo, and Leandro Aolita, "Randomized semi-quantum matrix processing", npj Quantum Information 10 1, 93 (2024).

[174] S E Skelton, "von Neumann measurement and quantum phase estimation of block-encoded Hamiltonians", Quantum Science and Technology 11 3, 035014 (2026).

[175] Mark Steudtner, Sam Morley-Short, William Pol, Sukin Sim, Cristian L. Cortes, Matthias Loipersberger, Robert M. Parrish, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Fault-tolerant quantum computation of molecular observables", Quantum 7, 1164 (2023).

[176] Jia-Chen Tang, Xu-Yang Hou, Yu-Huan Huang, Hao Guo, and Chih-Chun Chien, "Evolution of quantum geometric tensor of one-dimensional periodic systems after a quench", Physical Review B 113 17, 174301 (2026).

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

[178] 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).

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

[180] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[181] Lindsay Bassman, 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).

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

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

[184] Sam McArdle, András Gilyén, and Mario Berta, "A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits", arXiv:2209.12887, (2022).

[185] Yiyi Cai, Yu Tong, and John Preskill, "Stochastic Error Cancellation in Analog Quantum Simulation", arXiv:2311.14818, (2023).

[186] Kianna Wan and Isaac H. Kim, "Fast digital methods for adiabatic state preparation", arXiv:2004.04164, (2020).

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

[188] Jordi Weggemans, Marten Folkertsma, and Chris Cade, "Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture", arXiv:2302.11578, (2023).

[189] Pei Zeng, Jinzhao Sun, Liang Jiang, and Qi Zhao, "Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations", arXiv:2212.04566, (2022).

[190] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "On the complexity of implementing Trotter steps", arXiv:2211.09133, (2022).

[191] Roberto Campos, "Hybrid Quantum-Classical Algorithms", arXiv:2406.12371, (2024).

[192] Daochen Wang, Xuchen You, Tongyang Li, and Andrew M. Childs, "Quantum exploration algorithms for multi-armed bandits", arXiv:2007.07049, (2020).

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

[194] Taehee Ko and Sungbin Lim, "Analytic and Stochastic Approach to Quantum Advantages in Ground State and Quantum State Preparation Problems", arXiv:2510.01563, (2025).

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The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 15:20:34) and SAO/NASA ADS (last updated successfully 2026-07-15 15:20:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

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