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] Michael R. Geller, Zoë Holmes, Patrick J. Coles, and Andrew Sornborger, "Experimental quantum learning of a spectral decomposition", Physical Review Research 3 3, 033200 (2021).

[63] Leonardo Novo, "Bridging gaps between random approaches to quantum simulation", Quantum Views 4, 33 (2020).

[64] Lawrence Z. Cohen, Isaac H. Kim, Stephen D. Bartlett, and Benjamin J. Brown, "Low-overhead fault-tolerant quantum computing using long-range connectivity", Science Advances 8 20, eabn1717 (2022).

[65] Quynh T. Nguyen, Bobak T. Kiani, and Seth Lloyd, "Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra", Quantum 6, 876 (2022).

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

[67] Yanbing Zhang, Tingting Song, and Zhihao Wu, "An improved algorithm for computing hitting probabilities of quantum walks", Physica A: Statistical Mechanics and its Applications 594, 127009 (2022).

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

[70] Guru-Vamsi Policharla and Sai Vinjanampathy, "Algorithmic Primitives for Quantum-Assisted Quantum Control", Physical Review Letters 127 22, 220504 (2021).

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

[72] 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).

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

[74] Priyanka Mukhopadhyay, Torin F. Stetina, and Nathan Wiebe, "Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian", PRX Quantum 5 1, 010345 (2024).

[75] 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).

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

[77] Valentina Amitrano, Alessandro Roggero, Piero Luchi, Francesco Turro, Luca Vespucci, and Francesco Pederiva, "Trapped-ion quantum simulation of collective neutrino oscillations", Physical Review D 107 2, 023007 (2023).

[78] V. M. Bastidas, S. Zeytinoğlu, Z. M. Rossi, I. L. Chuang, and W. J. Munro, "Quantum signal processing with the one-dimensional quantum Ising model", Physical Review B 109 1, 014306 (2024).

[79] Cristian L. Cortes and Stephen K. Gray, "Quantum Krylov subspace algorithms for ground- and excited-state energy estimation", Physical Review A 105 2, 022417 (2022).

[80] 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).

[81] 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).

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

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

[84] 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).

[85] 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).

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

[87] Thomas E. Baker, "Lanczos recursion on a quantum computer for the Green's function and ground state", Physical Review A 103 3, 032404 (2021).

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

[89] 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).

[90] 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).

[91] 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).

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

[93] Dominic W. Berry, Yuan Su, Casper Gyurik, Robbie King, Joao Basso, Alexander Del Toro Barba, Abhishek Rajput, Nathan Wiebe, Vedran Dunjko, and Ryan Babbush, "Analyzing Prospects for Quantum Advantage in Topological Data Analysis", PRX Quantum 5 1, 010319 (2024).

[94] Karuna Kadian, Sunita Garhwal, and Ajay Kumar, "Quantum walk and its application domains: A systematic review", Computer Science Review 41, 100419 (2021).

[95] Tatsuki Odake, Hlér Kristjánsson, Akihito Soeda, and Mio Murao, "Higher-order quantum transformations of Hamiltonian dynamics", Physical Review Research 6 1, L012063 (2024).

[96] Alessandro Summer, Cecilia Chiaracane, Mark T. Mitchison, and John Goold, "Calculating the many-body density of states on a digital quantum computer", Physical Review Research 6 1, 013106 (2024).

[97] Priyanka Mukhopadhyay, "Composability of global phase invariant distance and its application to approximation error management", Journal of Physics Communications 5 11, 115017 (2021).

[98] Michael Kreshchuk, William M. Kirby, Gary Goldstein, Hugo Beauchemin, and Peter J. Love, "Quantum simulation of quantum field theory in the light-front formulation", Physical Review A 105 3, 032418 (2022).

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

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

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

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

[103] 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).

[104] Yuanye Zhu, "Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation", Entropy 25 1, 62 (2022).

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

[106] Daan Camps, Lin Lin, Roel Van Beeumen, and Chao Yang, "Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices", SIAM Journal on Matrix Analysis and Applications 45 1, 801 (2024).

[107] Matthew Otten, Byeol Kang, Dmitry Fedorov, Joo-Hyoung Lee, Anouar Benali, Salman Habib, Stephen K. Gray, and Yuri Alexeev, "QREChem: quantum resource estimation software for chemistry applications", Frontiers in Quantum Science and Technology 2, 1232624 (2023).

[108] Alexander M. Dalzell, B. David Clader, Grant Salton, Mario Berta, Cedric Yen-Yu Lin, David A. Bader, Nikitas Stamatopoulos, Martin J. A. Schuetz, Fernando G. S. L. Brandão, Helmut G. Katzgraber, and William J. Zeng, "End-To-End Resource Analysis for Quantum Interior-Point Methods and Portfolio Optimization", PRX Quantum 4 4, 040325 (2023).

[109] Kenneth Choi, Dean Lee, Joey Bonitati, Zhengrong Qian, and Jacob Watkins, "Rodeo Algorithm for Quantum Computing", Physical Review Letters 127 4, 040505 (2021).

[110] 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).

[111] Abhijeet Alase, Owen Doty, and David L. Feder, "Matrix permanent and determinant from a spin system", Physical Review A 108 1, 012207 (2023).

[112] 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).

[113] 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).

[114] 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).

[115] Nicholas C. Rubin, Dominic W. Berry, Fionn D. Malone, Alec F. White, Tanuj Khattar, A. Eugene DePrince, Sabrina Sicolo, Michael Küehn, Michael Kaicher, Joonho Lee, and Ryan Babbush, "Fault-Tolerant Quantum Simulation of Materials Using Bloch Orbitals", PRX Quantum 4 4, 040303 (2023).

[116] 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).

[117] Albert T. Schmitz, Nicolas P. D. Sawaya, Sonika Johri, and A. Y. Matsuura, "Graph optimization perspective for low-depth Trotter-Suzuki decomposition", Physical Review A 109 4, 042418 (2024).

[118] 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).

[119] Hari Krovi, "Improved quantum algorithms for linear and nonlinear differential equations", Quantum 7, 913 (2023).

[120] Sam McArdle, "Learning from Physics Experiments with Quantum Computers: Applications in Muon Spectroscopy", PRX Quantum 2 2, 020349 (2021).

[121] Nick S. Blunt, Joan Camps, Ophelia Crawford, Róbert Izsák, Sebastian Leontica, Arjun Mirani, Alexandra E. Moylett, Sam A. Scivier, Christoph Sünderhauf, Patrick Schopf, Jacob M. Taylor, and Nicole Holzmann, "Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications", Journal of Chemical Theory and Computation 18 12, 7001 (2022).

[122] I. Meyerov, A. Liniov, M. Ivanchenko, and S. Denisov, "Modeling Complex Quantum Dynamics: Evolution of Numerical Algorithms in the HPC Context", Lobachevskii Journal of Mathematics 41 8, 1509 (2020).

[123] Shang Gao, Shi-Jie Pan, Guang-Bao Xu, and Yu-Guang Yang, "Quantum average neighborhood margin maximization for feature extraction", Quantum Information Processing 22 3, 152 (2023).

[124] 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).

[125] Thomas E. Baker and David Poulin, "Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer", Physical Review Research 2 4, 043238 (2020).

[126] Xiantao Li and Chunhao Wang, "Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems", Communications in Mathematical Physics 401 1, 147 (2023).

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

[128] Christian W. Bauer, Zohreh Davoudi, A. Baha Balantekin, Tanmoy Bhattacharya, Marcela Carena, Wibe A. de Jong, Patrick Draper, Aida El-Khadra, Nate Gemelke, Masanori Hanada, Dmitri Kharzeev, Henry Lamm, Ying-Ying Li, Junyu Liu, Mikhail Lukin, Yannick Meurice, Christopher Monroe, Benjamin Nachman, Guido Pagano, John Preskill, Enrico Rinaldi, Alessandro Roggero, David I. Santiago, Martin J. Savage, Irfan Siddiqi, George Siopsis, David Van Zanten, Nathan Wiebe, Yukari Yamauchi, Kübra Yeter-Aydeniz, and Silvia Zorzetti, "Quantum Simulation for High-Energy Physics", PRX Quantum 4 2, 027001 (2023).

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

[130] 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, 052627 (2024).

[131] 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).

[132] 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).

[133] 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).

[134] 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).

[135] 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).

[136] 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).

[137] 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).

[138] 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).

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

[140] 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).

[141] 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).

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

[143] 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).

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

[145] 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).

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

[147] 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).

[148] 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).

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

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

[151] 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).

[152] 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).

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

[154] 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).

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

[156] 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).

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

[158] 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).

[159] 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).

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

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

[162] 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).

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

[164] 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).

[165] 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).

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

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

[168] 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).

[169] 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).

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

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

[172] 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).

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

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

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

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

[178] 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).

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

[180] 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).

[181] 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).

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[183] 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).

[184] 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 acs.jctc.4c00352 (2024).

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

[186] 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).

[187] 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).

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[189] 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).

[190] 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).

[191] 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).

[192] 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.

[193] 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).

[194] 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).

[195] 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).

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

[197] 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).

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

[200] 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).

[201] 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).

[202] 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).

[203] 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.

[204] 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).

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

[206] 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).

[207] 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).

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

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

[210] 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).

[211] 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).

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

[213] 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).

[214] 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).

[215] 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).

[216] 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).

[217] 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).

[218] 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).

[219] 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).

[220] Savo Glisic and Beatriz Lorenzo, "Quantum Computing and Neuroscience for 6G/7G Networks: Survey", Intelligent Systems with Applications 200346 (2024).

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

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

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

[224] 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).

[225] 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).

[226] 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).

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

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

[229] 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).

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

[231] 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).

[232] 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).

[233] 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).

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

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

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

[237] 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).

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

[239] 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).

[240] 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).

[241] 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).

[242] 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).

[243] 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).

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

[245] 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).

[246] Fabian Langkabel and Annika Bande, "Quantum-Compute Algorithm for Exact Laser-Driven Electron Dynamics in Molecules", Journal of Chemical Theory and Computation 18 12, 7082 (2022).

[247] 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).

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

[249] 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).

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

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

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

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[254] 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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[258] Ruizhe Zhang, Guoming Wang, and Peter Johnson, "Computing Ground State Properties with Early Fault-Tolerant Quantum Computers", Quantum 6, 761 (2022).

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

[260] 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).

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

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

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

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

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

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

[278] 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).

[279] 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).

[280] 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).

[281] 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).

[282] 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).

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[285] 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).

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

[288] 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).

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[292] 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).

[293] Alexander Engel, Graeme Smith, and Scott E. Parker, "Quantum algorithm for the Vlasov equation", Physical Review A 100 6, 062315 (2019).

[294] 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).

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

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[302] 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).

[303] Oriel Kiss, Michele Grossi, and Alessandro Roggero, "Importance sampling for stochastic quantum simulations", Quantum 7, 977 (2023).

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

[306] Annika Bande, Chemical Modelling 91 (2022) ISBN:978-1-83916-741-6.

[307] Aleksei V. Ivanov, Christoph Sünderhauf, Nicole Holzmann, Tom Ellaby, Rachel N. Kerber, Glenn Jones, and Joan Camps, "Quantum computation for periodic solids in second quantization", Physical Review Research 5 1, 013200 (2023).

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

[309] 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).

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

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

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

[313] 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).

[314] 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).

[315] Yuxiang Liu, Zaichen Zhang, Yi Hu, Fanxu Meng, Tian Luan, Xianchao Zhang, and Xutao Yu, "Practical circuit optimization algorithm for quantum simulation based on template matching", Quantum Information Processing 23 2, 45 (2024).

[316] 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).

[317] Yutaka Shikano, Hiroshi C. Watanabe, Ken M. Nakanishi, and Yu-ya Ohnishi, "Post-Hartree–Fock method in quantum chemistry for quantum computer", The European Physical Journal Special Topics 230 4, 1037 (2021).

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

[319] Richard Meister, Simon C. Benjamin, and Earl T. Campbell, "Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries", Quantum 6, 637 (2022).

[320] Chi-Fang Chen, Alexander M. Dalzell, Mario Berta, Fernando G. S. L. Brandão, and Joel A. Tropp, "Sparse Random Hamiltonians Are Quantumly Easy", Physical Review X 14 1, 011014 (2024).

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[322] Charles Yuan, Agnes Villanyi, and Michael Carbin, "Quantum Control Machine: The Limits of Control Flow in Quantum Programming", Proceedings of the ACM on Programming Languages 8 OOPSLA1, 1 (2024).

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[337] Giulia Meuli, Mathias Soeken, Martin Roetteler, and Thomas Häner, "Enabling accuracy-aware Quantum compilers using symbolic resource estimation", Proceedings of the ACM on Programming Languages 4 OOPSLA, 1 (2020).

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[339] Shouzhen Gu, Rolando D. Somma, and Burak Şahinoğlu, "Fast-forwarding quantum evolution", Quantum 5, 577 (2021).

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[341] Shantanav Chakraborty, Kyle Luh, and Jérémie Roland, "Analog quantum algorithms for the mixing of Markov chains", Physical Review A 102 2, 022423 (2020).

[342] Guglielmo Mazzola, "Quantum computing for chemistry and physics applications from a Monte Carlo perspective", The Journal of Chemical Physics 160 1, 010901 (2024).

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[344] 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).

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Hamiltonian Simulation by Qubitization

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