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

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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.

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[1] S. Lloyd, ``Universal Quantum Simulators,'' Science 273, 1073 (1996).

[2] D. Aharonov and A. Ta-Shma, ``Adiabatic quantum state generation and statistical zero knowledge,'' in Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03, STOC '03 (ACM Press, New York, New York, USA, 2003) p. 20.

[3] A. M. Childs and N. Wiebe, ``Hamiltonian Simulation Using Linear Combinations of Unitary Operations,'' Quantum Information & Computation 12, 901 (2012).

[4] D. W. Berry and A. M. Childs, ``Black-box Hamiltonian simulation and unitary implementation,'' Quantum Information & Computation 12, 29 (2012).

[5] S. Lloyd, M. Mohseni, and P. Rebentrost, ``Quantum principal component analysis,'' Nature Physics 10, 631 (2014).

[6] D. W. Berry, A. M. Childs, and R. Kothari, ``Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters,'' in 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS '15 (IEEE, Washington, DC, USA, 2015) pp. 792–809.

[7] G. H. Low and I. L. Chuang, ``Optimal Hamiltonian Simulation by Quantum Signal Processing,'' Physical Review Letters 118, 010501 (2017a).

[8] A. W. Harrow, A. Hassidim, and S. Lloyd, ``Quantum Algorithm for Linear Systems of Equations,'' Physical Review Letters 103, 150502 (2009).

[9] A. M. Childs, R. Kothari, and R. D. Somma, ``Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision,'' SIAM Journal on Computing 46, 1920 (2017).

[10] A. N. Chowdhury and R. D. Somma, ``Quantum algorithms for Gibbs sampling and hitting-time estimation,'' Quantum Information & Computation 17, 41 (2017).

[11] F. G. Brandao and K. M. Svore, ``Quantum Speed-Ups for Solving Semidefinite Programs,'' 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) , 415 (2017).

[12] M.-H. Yung, J. D. Whitfield, S. Boixo, D. G. Tempel, and A. Aspuru-Guzik, ``Introduction to Quantum Algorithms for Physics and Chemistry,'' in Quantum Information and Computation for Chemistry (John Wiley & Sons, Inc., 2014) pp. 67–106.

[13] D. Wecker, B. Bauer, B. K. Clark, M. B. Hastings, and M. Troyer, ``Gate-count estimates for performing quantum chemistry on small quantum computers,'' Physical Review A 90, 022305 (2014).

[14] D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, ``The Trotter step size required for accurate quantum simulation of quantum chemistry,'' Quantum Information & Computation 15, 361 (2015).

[15] M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, ``Elucidating reaction mechanisms on quantum computers,'' Proceedings of the National Academy of Sciences 114, 7555 (2017).

[16] R. Babbush, D. W. Berry, I. D. Kivlichan, A. Y. Wei, P. J. Love, and A. Aspuru-Guzik, ``Exponentially more precise quantum simulation of fermions in second quantization,'' New Journal of Physics 18, 033032 (2016).

[17] I. D. Kivlichan, N. Wiebe, R. Babbush, and A. Aspuru-Guzik, ``Bounding the costs of quantum simulation of many-body physics in real space,'' Journal of Physics A: Mathematical and Theoretical 50, 305301 (2017).

[18] P. J. J. O'Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V. Coveney, P. J. Love, H. Neven, A. Aspuru-Guzik, and J. M. Martinis, ``Scalable Quantum Simulation of Molecular Energies,'' Physical Review X 6, 031007 (2016).

[19] R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O'Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, ``Superconducting quantum circuits at the surface code threshold for fault tolerance,'' Nature 508, 500 (2014).

[20] S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, ``Demonstration of a small programmable quantum computer with atomic qubits,'' Nature 536, 63 (2016).

[21] D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, ``Exponential improvement in precision for simulating sparse Hamiltonians,'' in Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14, STOC '14 (ACM Press, New York, New York, USA, 2014) pp. 283–292.

[22] D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, ``Simulating Hamiltonian Dynamics with a Truncated Taylor Series,'' Physical Review Letters 114, 090502 (2015b).

[23] A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, ``Exponential algorithmic speedup by a quantum walk,'' in Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03, STOC '03 (ACM Press, New York, New York, USA, 2003) p. 59.

[24] A. M. Childs, ``On the Relationship Between Continuous- and Discrete-Time Quantum Walk,'' Communications in Mathematical Physics 294, 581 (2010).

[25] R. Kothari, Efficient algorithms in quantum query complexity, Ph.D. thesis, University of Waterloo (2014).

[26] M. Szegedy, ``Spectra of Quantized Walks and a $\sqrt{\delta\epsilon}$ rule,'' arXiv preprint quant-ph/​0401053 (2004a).

[27] D. W. Berry and L. Novo, ``Corrected Quantum Walk for Optimal Hamiltonian Simulation,'' Quantum Information & Computation 16, 1295 (2016).

[28] S. Kimmel, C. Y.-Y. Lin, G. H. Low, M. Ozols, and T. J. Yoder, ``Hamiltonian simulation with optimal sample complexity,'' npj Quantum Information 3, 13 (2017).

[29] S. Chakraborty, A. Gilyén, and S. Jeffery, ``The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation,'' arXiv preprint arXiv:1804.01973 (2018).
arXiv:1804.01973 http://arxiv.org/abs/1804.01973

[30] R. D. Somma and S. Boixo, ``Spectral Gap Amplification,'' SIAM Journal on Computing 42, 593 (2013).

[31] M. Szegedy, ``Quantum Speed-Up of Markov Chain Based Algorithms,'' in 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS '04 (IEEE, Washington, DC, USA, 2004) pp. 32–41.

[32] A. Daskin and S. Kais, ``An ancilla-based quantum simulation framework for non-unitary matrices,'' Quantum Information Processing 16, 33 (2017).

[33] G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Springer Tracts in Natural Philosophy, Vol. 13 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1967).

[34] L. K. Grover, ``A fast quantum mechanical algorithm for database search,'' Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 STOC '96, 212 (1996).

[35] T. J. Yoder, G. H. Low, and I. L. Chuang, ``Fixed-Point Quantum Search with an Optimal Number of Queries,'' Physical Review Letters 113, 210501 (2014).

[36] J. McClellan, T. Parks, and L. Rabiner, ``A computer program for designing optimum FIR linear phase digital filters,'' IEEE Transactions on Audio and Electroacoustics 21, 506 (1973).

[37] G. H. Low, T. J. Yoder, and I. L. Chuang, ``Methodology of Resonant Equiangular Composite Quantum Gates,'' Physical Review X 6, 041067 (2016).

[38] M. Abramowitz, I. A. Stegun, and Others, ``Handbook of mathematical functions,'' Applied mathematics series 55, 62 (1966).

[39] J. P. Boyd, ``Rootfinding for a transcendental equation without a first guess: Polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine,'' Applied Numerical Mathematics 57, 12 (2007).

[40] A. M. Childs and R. Kothari, ``Limitations on the Simulation of Non-sparse Hamiltonians,'' Quantum Information & Computation 10, 669 (2010).

[41] R. D. Somma, ``A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation,'' Journal of Mathematical Physics 57, 062202 (2016).

[42] G. H. Low, T. J. Yoder, and I. L. Chuang, ``Quantum Imaging by Coherent Enhancement,'' Physical Review Letters 114, 100801 (2015).

[43] A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, ``Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,'' in Proceedings of the 51st Annual ACM Symposium on Theory of Computing - STOC '19 (ACM Press, New York, New York, USA, 2019) pp. 193–204.

[44] J. Haah, M. Hastings, R. Kothari, and G. H. Low, ``Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians,'' in 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), FOCS '18 (IEEE, Washington, DC, USA, 2018) pp. 350–360.

[45] A. M. Childs and Y. Su, ``Nearly optimal lattice simulation by product formulas,'' arXiv preprint arXiv:1901.00564 (2019).

[46] G. H. Low and I. L. Chuang, ``Hamiltonian Simulation by Uniform Spectral Amplification,'' arXiv preprint arXiv:1707.05391 (2017b).

[47] G. H. Low, ``Hamiltonian simulation with nearly optimal dependence on spectral norm,'' in Proceedings of the 51st Annual ACM Symposium on Theory of Computing - STOC '19 (ACM Press, New York, New York, USA, 2019) pp. 491–502.

[48] G. H. Low and N. Wiebe, ``Hamiltonian Simulation in the Interaction Picture,'' arXiv preprint arXiv:1805.00675 (2018).

[49] A. M. Childs, D. Maslov, Y. Nam, N. J. Ross, and Y. Su, ``Toward the first quantum simulation with quantum speedup,'' Proceedings of the National Academy of Sciences 115, 9456 (2018).

[50] J. Haah, ``Product Decomposition of Periodic Functions in Quantum Signal Processing,'' arXiv preprint arXiv:1806.10236 (2018).

[51] L. J. Karam and J. H. McClellan, ``Chebyshev digital FIR filter design,'' Signal Processing 76, 17 (1999).

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[82] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

[83] 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).

[84] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe, "Time-dependent Hamiltonian simulation withL1-norm scaling", arXiv:1906.07115, Quantum 4, 254 (2020).

[85] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, Reviews of Modern Physics 92 1, 015003 (2020).

[86] William M. Kirby and Peter J. Love, "Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers", Physical Review Letters 123 20, 200501 (2019).

[87] 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).

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

[89] Jeongwan Haah, "Product Decomposition of Periodic Functions in Quantum Signal Processing", arXiv:1806.10236, Quantum 3, 190 (2019).

[90] 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).

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

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

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

[94] I. Y. Dodin and E. A. Startsev, "On applications of quantum computing to plasma simulations", Physics of Plasmas 28 9, 092101 (2021).

[95] Alexis Ralli, Peter J. Love, Andrew Tranter, and Peter V. Coveney, "Implementation of measurement reduction for the variational quantum eigensolver", Physical Review Research 3 3, 033195 (2021).

[96] 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).

[97] 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).

[98] 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).

[99] 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).

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

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

[102] 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).

[103] Jeongwan Haah, Matthew B. Hastings, Robin Kothari, and Guang Hao Low, "Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians", arXiv:1801.03922, SIAM Journal on Computing FOCS18-250 (2021).

[104] Chee-Kong Lee, Jonathan Wei Zhong Lau, Liang Shi, and Leong Chuan Kwek, "Simulating Energy Transfer in Molecular Systems with Digital Quantum Computers", Journal of Chemical Theory and Computation 18 3, 1347 (2022).

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

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

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

[108] 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).

[109] Alexander Miessen, Pauline J. Ollitrault, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics: A performance study on the spin-boson model", Physical Review Research 3 4, 043212 (2021).

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

[111] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, "Nearly tight Trotterization of interacting electrons", arXiv:2012.09194, Quantum 5, 495 (2021).

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

[113] Andrew M. Childs, Aaron Ostrander, and Yuan Su, "Faster quantum simulation by randomization", arXiv:1805.08385, Quantum 3, 182 (2019).

[114] Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf, "Quantum SDP-Solvers: Better upper and lower bounds", arXiv:1705.01843, Quantum 4, 230 (2020).

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

[116] 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).

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

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

[119] 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).

[120] 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", arXiv:1808.02625, npj Quantum Information 7 1, 83 (2021).

[121] 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).

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

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

[124] 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).

[125] 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).

[126] Samuel Jaques and Thomas Häner, "Leveraging state sparsity for more efficient quantum simulations", ACM Transactions on Quantum Computing 3491248 (2022).

[127] Rolando D Somma, "Quantum eigenvalue estimation via time series analysis", arXiv:1907.11748, New Journal of Physics 21 12, 123025 (2019).

[128] Changhao Yi, "Success of digital adiabatic simulation with large Trotter step", Physical Review A 104 5, 052603 (2021).

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

[130] Abhoy Kole and Indranil Sengupta, 2020 IEEE International Test Conference India 1 (2020) ISBN:978-1-7281-7458-7.

[131] Patrick Rall, "Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation", arXiv:2103.09717, Quantum 5, 566 (2021).

[132] 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).

[133] 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).

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

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

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

[137] 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).

[138] 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).

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

[140] 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).

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

[142] Qingfeng Wang, Ming Li, Christopher Monroe, and Yunseong Nam, "Resource-Optimized Fermionic Local-Hamiltonian Simulation on a Quantum Computer for Quantum Chemistry", Quantum 5, 509 (2021).

[143] 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).

[144] 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).

[145] 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).

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

[147] 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).

[148] Carlos Outeiral, Martin Strahm, Jiye Shi, Garrett M. Morris, Simon C. Benjamin, and Charlotte M. Deane, "The prospects of quantum computing in computational molecular biology", WIREs Computational Molecular Science 11 1(2021).

[149] 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).

[150] 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).

[151] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, "A Theory of Trotter Error", arXiv:1912.08854.

[152] 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).

[153] Guoming Wang, "Quantum algorithm for linear regression", arXiv:1402.0660, Physical Review A 96 1, 012335 (2017).

[154] 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.

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

[156] 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).

[157] Guang Hao Low and Nathan Wiebe, "Hamiltonian Simulation in the Interaction Picture", arXiv:1805.00675.

[158] Natalie Klco and Martin J. Savage, "Digitization of scalar fields for quantum computing", arXiv:1808.10378, Physical Review A 99 5, 052335 (2019).

[159] Andrew Shaw, "Classical-Quantum Noise Mitigation for NISQ Hardware", arXiv:2105.08701.

[160] Bojia Duan, Jiabin Yuan, Chao-Hua Yu, Jianbang Huang, and Chang-Yu Hsieh, "A survey on HHL algorithm: From theory to application in quantum machine learning", Physics Letters A 384, 126595 (2020).

[161] Vedran Dunjko and Hans J. Briegel, "Machine learning \& artificial intelligence in the quantum domain", arXiv:1709.02779.

[162] Changpeng Shao, "An Improved Algorithm for Quantum Principal Component Analysis", arXiv:1903.03999.

[163] Shantanav Chakraborty, András Gilyén, and Stacey Jeffery, "The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation", arXiv:1804.01973.

[164] Danial Dervovic, Mark Herbster, Peter Mountney, Simone Severini, Naïri Usher, and Leonard Wossnig, "Quantum linear systems algorithms: a primer", arXiv:1802.08227.

[165] David Poulin, Alexei Kitaev, Damian S. Steiger, Matthew B. Hastings, and Matthias Troyer, "Quantum Algorithm for Spectral Measurement with a Lower Gate Count", Physical Review Letters 121 1, 010501 (2018).

[166] Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, and Yuan Su, "Toward the first quantum simulation with quantum speedup", arXiv:1711.10980.

[167] Andrew Shaw, "Benchmarking Quantum Simulators", arXiv:2110.13025.

[168] Dominic W. Berry, Mária Kieferová, Artur Scherer, Yuval R. Sanders, Guang Hao Low, Nathan Wiebe, Craig Gidney, and Ryan Babbush, "Improved techniques for preparing eigenstates of fermionic Hamiltonians", npj Quantum Information 4, 22 (2018).

[169] 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).

[170] Guang Hao Low and Isaac L. Chuang, "Hamiltonian Simulation by Uniform Spectral Amplification", arXiv:1707.05391.

[171] 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", arXiv:1812.09976.

[172] Suguru Endo, Qi Zhao, Ying Li, Simon Benjamin, and Xiao Yuan, "Mitigating algorithmic errors in a Hamiltonian simulation", arXiv:1808.03623, Physical Review A 99 1, 012334 (2019).

[173] Patrick Rebentrost, Maria Schuld, Leonard Wossnig, Francesco Petruccione, and Seth Lloyd, "Quantum gradient descent and Newton's method for constrained polynomial optimization", arXiv:1612.01789.

[174] Guang Hao Low, Nicholas P. Bauman, Christopher E. Granade, Bo Peng, Nathan Wiebe, Eric J. Bylaska, Dave Wecker, Sriram Krishnamoorthy, Martin Roetteler, Karol Kowalski, Matthias Troyer, and Nathan A. Baker, "Q# and NWChem: Tools for Scalable Quantum Chemistry on Quantum Computers", arXiv:1904.01131.

[175] Hrant Gharibyan, Masanori Hanada, Masazumi Honda, and Junyu Liu, "Toward simulating superstring/M-theory on a quantum computer", Journal of High Energy Physics 2021 7, 140 (2021).

[176] Ryan Babbush, Dominic W. Berry, and Hartmut Neven, "Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization", Physical Review A 99 4, 040301 (2019).

[177] Scott E. Smart and David A. Mazziotti, "Many-Fermion Simulation from the Contracted Quantum Eigensolver without Fermionic Encoding of the Wave Function", arXiv:2205.01725.

[178] Ian D. Kivlichan, Nathan Wiebe, Ryan Babbush, and Alán Aspuru-Guzik, "Bounding the costs of quantum simulation of many-body physics in real space", Journal of Physics A Mathematical General 50 30, 305301 (2017).

[179] Junyu Liu, Jinzhao Sun, and Xiao Yuan, "Towards a variational Jordan-Lee-Preskill quantum algorithm", arXiv:2109.05547.

[180] Jinfeng Zeng, Chenfeng Cao, Chao Zhang, Pengxiang Xu, and Bei Zeng, "A variational quantum algorithm for Hamiltonian diagonalization", Quantum Science and Technology 6 4, 045009 (2021).

[181] Joran van Apeldoorn and András Gilyén, "Improvements in Quantum SDP-Solving with Applications", arXiv:1804.05058.

[182] Guang Hao Low, Vadym Kliuchnikov, and Luke Schaeffer, "Trading T-gates for dirty qubits in state preparation and unitary synthesis", arXiv:1812.00954.

[183] Guang Hao Low, Theodore J. Yoder, and Isaac L. Chuang, "Methodology of Resonant Equiangular Composite Quantum Gates", Physical Review X 6 4, 041067 (2016).

[184] Yimin Ge, Jordi Tura, and J. Ignacio Cirac, "Faster ground state preparation and high-precision ground energy estimation with fewer qubits", arXiv:1712.03193, Journal of Mathematical Physics 60 2, 022202 (2019).

[185] András Gilyén, Seth Lloyd, Iman Marvian, Yihui Quek, and Mark M. Wilde, "Quantum algorithm for Petz recovery channels and pretty good measurements", arXiv:2006.16924.

[186] Nicholas P. Bauman, Eric J. Bylaska, Sriram Krishnamoorthy, Guang Hao Low, Nathan Wiebe, Christopher E. Granade, Martin Roetteler, Matthias Troyer, and Karol Kowalski, "Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms", Journal of Chemical Physics 151 1, 014107 (2019).

[187] Ronald de Wolf, "Quantum Computing: Lecture Notes", arXiv:1907.09415.

[188] Teng Bian, Daniel Murphy, Rongxin Xia, Ammar Daskin, and Sabre Kais, "Quantum computing methods for electronic states of the water molecule", Molecular Physics 117 15-16, 2069 (2019).

[189] Rui Chao, Dawei Ding, Andras Gilyen, Cupjin Huang, and Mario Szegedy, "Finding Angles for Quantum Signal Processing with Machine Precision", arXiv:2003.02831.

[190] Mária Kieferová, Artur Scherer, and Dominic W. Berry, "Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series", Physical Review A 99 4, 042314 (2019).

[191] Andrew M. Childs and Jin-Peng Liu, "Quantum Spectral Methods for Differential Equations", Communications in Mathematical Physics 375 2, 1427 (2020).

[192] Yuval R. Sanders, Guang Hao Low, Artur Scherer, and Dominic W. Berry, "Black-Box Quantum State Preparation without Arithmetic", arXiv:1807.03206, Physical Review Letters 122 2, 020502 (2019).

[193] Laura Clinton, Johannes Bausch, and Toby Cubitt, "Hamiltonian simulation algorithms for near-term quantum hardware", Nature Communications 12, 4989 (2021).

[194] Ryan Babbush, Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, and Garnet Kin-Lic Chan, "Low Depth Quantum Simulation of Electronic Structure", arXiv:1706.00023.

[195] Jarrod R. McClean, Fabian M. Faulstich, Qinyi Zhu, Bryan O'Gorman, Yiheng Qiu, Steven R. White, Ryan Babbush, and Lin Lin, "Discontinuous Galerkin discretization for quantum simulation of chemistry", New Journal of Physics 22 9, 093015 (2020).

[196] Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", arXiv:1808.02892.

[197] Xiu Gu, Jonathan Allcock, Shuoming An, and Yu-xi Liu, "Efficient multi-qubit subspace rotations via topological quantum walks", arXiv:2111.06534.

[198] Andrew M. Childs, Jiaqi Leng, Tongyang Li, Jin-Peng Liu, and Chenyi Zhang, "Quantum simulation of real-space dynamics", arXiv:2203.17006.

[199] Seth Lloyd, Bobak T. Kiani, David R. M. Arvidsson-Shukur, Samuel Bosch, Giacomo De Palma, William M. Kaminsky, Zi-Wen Liu, and Milad Marvian, "Hamiltonian singular value transformation and inverse block encoding", arXiv:2104.01410.

[200] Qisheng Wang, Zhicheng Zhang, Kean Chen, Ji Guan, Wang Fang, and Mingsheng Ying, "Quantum Algorithm for Fidelity Estimation", arXiv:2103.09076.

[201] Sathyawageeswar Subramanian, Stephen Brierley, and Richard Jozsa, "Implementing smooth functions of a Hermitian matrix on a quantum computer", Journal of Physics Communications 3 6, 065002 (2019).

[202] Alexander J. Buser, Hrant Gharibyan, Masanori Hanada, Masazumi Honda, and Junyu Liu, "Quantum simulation of gauge theory via orbifold lattice", arXiv:2011.06576.

[203] Alessandro Roggero and Joseph Carlson, "Linear Response on a Quantum Computer", arXiv:1804.01505.

[204] Jue Xu, "On Lagrangian Formalism of Quantum Computation", arXiv:2112.04892.

[205] Guang Hao Low, "Hamiltonian simulation with nearly optimal dependence on spectral norm", arXiv:1807.03967.

[206] Yihui Quek and Patrick Rebentrost, "Fast algorithm for quantum polar decomposition, pretty-good measurements, and the Procrustes problem", arXiv:2106.07634.

[207] Leonardo Novo and Dominic W. Berry, "Improved Hamiltonian simulation via a truncated Taylor series and corrections", arXiv:1611.10033.

[208] Alex Parent, Martin Roetteler, and Michele Mosca, "Improved reversible and quantum circuits for Karatsuba-based integer multiplication", arXiv:1706.03419.

[209] Ian D. Kivlichan, Christopher E. Granade, and Nathan Wiebe, "Phase estimation with randomized Hamiltonians", arXiv:1907.10070.

[210] Seth Lloyd and Reevu Maity, "Efficient implementation of unitary transformations", arXiv:1901.03431.

[211] Shalev Ben-David, Andrew M. Childs, András Gilyén, William Kretschmer, Supartha Podder, and Daochen Wang, "Symmetries, graph properties, and quantum speedups", arXiv:2006.12760.

[212] Ammar Daskin and Sabre Kais, "A generalized circuit for the Hamiltonian dynamics through the truncated series", Quantum Information Processing 17 12, 328 (2018).

[213] András Gilyén and Tongyang Li, "Distributional property testing in a quantum world", arXiv:1902.00814.

[214] Zhikuan Zhao, "Quantum Statistical Inference", arXiv:1812.04877.

[215] François Fillion-Gourdeau, Steve MacLean, and Raymond Laflamme, "Efficient state initialization by a quantum spectral filtering algorithm", Physical Review A 95 4, 042331 (2017).

[216] Nolan J. Coble and Matthew Coudron, "Quasi-polynomial time approximation of output probabilities of geometrically-local, shallow quantum circuits", arXiv:2012.05460.

[217] András Gilyén and Alexander Poremba, "Improved Quantum Algorithms for Fidelity Estimation", arXiv:2203.15993.

[218] Bill Poirier and Jonathan Jerke, "Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach", Physical Chemistry Chemical Physics (Incorporating Faraday Transactions) 24 7, 4437 (2022).

[219] M. B. Hastings, "The Short Path Algorithm Applied to a Toy Model", arXiv:1901.03884.

The above citations are from Crossref's cited-by service (last updated successfully 2022-05-18 07:11:24) and SAO/NASA ADS (last updated successfully 2022-05-18 07:11:25). The list may be incomplete as not all publishers provide suitable and complete citation data.